Martha,
Generally, in SOP the Red/Black wires are track power, opposite rails.
These would be on opposite ends of the decoder, left and right respectively, outermost tabs. Either front or rear, depending on which truck.

HOWEVER:
Any way you could post a pic? I'm not sure what the small gold cylinder would be referring too, and sometimes the factory wiring can vary from SOP.

If they do not belong where I mentioned, you will fry decoder, or other electronics.

Bachmann has had many iterations of this unit. I have two "Spectrum" versions, from pre-dcc days, and converted the one over to DCC when I switched over to it many years ago.

The second one has sat in the "round to it" stack, and just has stayed there. Those original (DC Only) Spectrum ones were not to easiest units to convert over back then, nor now...

I also have a pair of Atlas ones, one sitting in that "round to it" stack awaiting a decoder, paint and decals.

I kind of figured the warranty might have a wrinkle like that, but I could not beat his NOS "show (cash) only" price for it.

(Let's just say I expected to buy some NWSL replacement gears anyways, and would still come out ahead. Helps to know vendors and shop those ones every time you see them somewhere... They will throw a bone your way if they have something they are tired of lugging around everywhere if they have seen you often enough. Have got many really sweet deals that way. And at one really poorly run show, pointed in the direction of the head honcho, but that's another story....)

Thanks for the repair link.

If it is an ESU "Blank" sound decoder, the only way to install sound files is using their LokProgrammer.

There is also the Soundtraxx Tsunami-2 (What Athearn Genesis Factory sound units come with) 21 pin decoders, part number 885823. This would be the "EMD-2" sound set, where the 710-16 cyl. sound fits your locomotive. (CV 123=7 this decoder)
YankeeDabbler and Tony's Train Exchange both show as having a few of this one on hand, unsure on other retailers. (Not affiliated with them, just have used them before for decoder purchases.)

(Tony's can also assist in correct sized speaker if you call them. Round enclosure is generally 28mm in Genesis locomotive units IIRC.)

TCS (WowSound) also makes 21 pin sound decoders, but I did not see the correct one in stock to get a part number.

The SV decoders sometimes do not support all CV's.
Sorry.

ESU 58419 is the latest 21 pin Loksound, and includes a "sugar cube" style speaker and enclosure.
ESU 58429 is the same decoder, but no sugar cube speaker, allowing other sized 8 ohm speakers to be used in the place of the sugar cube.
(I am not 100% sure what size the SD70 would normally use. Bigger speakers will produce better sound.)

You will need to have the correct sound file loaded onto it. It would be the "EMD 16-710G3B LATE EXH T" sound file "S0720".

Many retailers will load the sound file for you.

On the 4-6-2, there is not an option for "sound starts at", but CV 113 is "quite Mode Timeout" value, where the sound will automatically shut off after so long of no commands to the address.
Default is 0, which is "off", you could adjust it up higher and see what value times it out at a good time for your style of operation, or continue using mute when you power up the layout.

CV 116 = 7 sets prime mover to start on speed step 1 according to DecoderPro.
(I do not have a SoundValue GP38-2 to test.)
Default is 39, so it might just work... If the SV decoder supports it.

As one who has a few of these models I can confirm they use the plastic clips.

My guess is one of the wires (or more) are loosely installed inside those clips.

Shell removal is easy. Unscrew and remove the two couplers and boxes, then remove two screws located in the chassis closest to the fuel tank. Entire shell assembly then slides right off.

Once the correct wire(s) are located and secured tightly, the problem should disappear.

The "click" is most likely one of a couple things: Either a cracked gear, flash inside the truck, or super dried out lube. (My guess is cracked gear. However, if these have not been run in years, it could be hardened lube.)

A single drop of LaBelle 108 (or similar) oil on the ends of the motor shafts will not hurt. (But only one very small drop!)
I know the trucks come apart, I just can not remember where the clip is located to disassemble. Once the bottom is popped off, lube access to the gears is much easier. (Again, very light lubrication is needed.) LaBelle 106 Grease (or similar) would be used here.

(Sorry Mr. Bach-mann.... I am unsure of your respective part numbers for these lubes.... I just happen to have these LaBelle lubes sitting on my workbench in front of me... But I am sure your lubes are nearly {if not perfectly} identical.)

Once the truck is disassembled, if there is dried out lube inside, pull the wheelsets out and scrub with Dawn dish-soapy water and a junk toothbrush, or use 70% Rubbing alcohol, to remove the old dried lube, let completely air dry, then reassemble and apply fresh new lube lightly. (The gearbox should not be packed with lube. That is way too much.)

(NOTE: I specify lightly lubed only because I have seen way too many new to the hobby way over lubricate locomotives. If you already know this, others who read this post might not.)

Your problem is simply size... Not power. Decoders are rated for a set speaker wattage. Any different causes issues. (Or does not work at all, damaging either decoder or speaker, or both, very quickly.)

Unfortunately, the small speakers have only finite sound volume available, before either not sounding right, or becoming damaged.

How big is the layout? If it's located in a single room and not that large, they do have systems that will play the locomotive sounds through much larger off-locomotive speakers, which will sound much better, and give more volume.
Or "MORE POWER" as "Time The Tool Man Taylor" says.  

That might be a better solution, depending on layout size and location.

Ok. I will be specific to your Genesis CR 2576 with this reply.

Non-sound will be easier first time installing than sound, but just barely. (No soldering required.)

This particular unit is indeed quick plug equipped, with a 21 pin plug. Any brand 21 pin decoder will simply be plug (and program) and play. (ESU, TCS, Digitrax, and Soundtraxx/Tsunami all make 21 pin decoders. With or without sound.) Genesis would come from the factory either DCC & Sound equipped, or DCC ready, no decoder installed. They use Soundtraxx Tsunami 2 decoders now, but any 21 pin decoder will work. (I prefer ESU, but others have other preferences. I think each brand has their fans.)

Your particular unit, if non-sound, is also DC Only at this point.

If you wish to install a 21 pin decoder in this model: You will need only a few small simple tools, being a pair of small tweezers, a smaller (jewelers/electronics repair style) size 0 Phillips screwdriver, along with the clamshell package the locomotive came in, the 21 pin decoder, and time and patience.

To remove the shell on this unit, unscrew and remove the two couplers and coupler boxes, and two additional screws located underneath near the fuel tank. (One in front, one in back, one left side, one right side. You will have to lightly rotate the trucks to gain access to these last two screws.) I recommend taking cell phone pics as you pull out the coupler boxes, to assist with reinstalling correctly oriented. (If desired, you can replace the plastic couplers with metal Kadee's at this time.)

Here is where the clamshell packaging is required:

If you still have the clamshell packaging, easiest way to avoid damaging the model is open the clamshell packaging "upside down", with the locomotive resting roof down in the top half of the clamshell packaging. Once these 4 screws are removed, the body shell is able to slide off of the chassis. (CAUTION: Light wires will still be connected to the shell. Do not yank hard on these thin wires.) Again, I recommend letting the shell rest roof down in the clamshell packaging to prevent any damage.
(There are foam cradles available, but if you have the original Genesis clamshell package, it is designed to hold the model without damaging it. Foam cradles, if used incorrectly, can damage details.) All 4 screws will be size 0 phillips heads.

Once the shell is removed from the chassis, you will see a circuit board mounted atop the motor, with multiple wires into it, with a separate smaller square circuit board plugged into it on the top. This is the DC "dummy" plug that gets pulled straight (and I do mean straight) up to remove. (Pulling at an angle will bend the little pins... Don't ask how I know this... So only pull straight up, no twisting or angling of the board.) The 21 pin decoder board will be the exact same size, just more "electronics" to it. It gets installed by pressing straight down over the pins, again taking care to not bend said pins. (This is literally the toughest part.)

If you are installing sound - Speaker wires will need soldered, following decoder manual instructions for placement. Non-sound will need zero wires soldered on this particular locomotive. The speaker location in this model will be specified in the parts diagram that came in the box. (I do not have a Genesis SD70... But if its the same Chassis as their SD70ACe is, I can get a picture for you if you chose to install sound.)

Once installed, simply slip the chassis and body shell back together (while taking care to not pinch wires) and reinstall the couplers, coupler boxes, and the 4 screws. (Tweezers will really come in handy holding these little screws into position.)

Then placing the locomotive on your programming track and programming the required settings (discussed more below) will have it ready to run.

I do recommend picking one decoder brand, and sticking to it with decoders that you install, (If you decide to) making consisting and programming easier to do consistently. Any decoder brand will work with your Digitrax DCC system. (Again, I default to ESU.)

Digitrax does make a PR4 programmer that can connect to any recent computer, via USB port, running freeware software known as DecoderPro (Uses JAVA platform) to assist with decoder programming. It will program all recent decoders, plus older version of almost every brand in existence. DecoderPro programming of decoders is very easy, as you simply select what you want the locomotive decoder to do, type in the address (Road number most times) you want, click through the options, and write to decoder using the computer programmer output on a totally separate track. (I highly recommend this for anyone adjusting any decoder settings, and use it myself on all non-ESU decoders I have in my Locomotive roster. It can also program ESU decoders as well. I just use the ESU specific programmer for their decoders, as it has more capabilities for their brand decoders.)
NOTE: Follow Digitrax Installation Instructions Carefully! Microsoft Windows is kinda dumb with this for whatever stupid reason...

(ESU also makes a computer programmer, but it is specific to only ESU decoders and uses only their program to do so. It does allow decoder firmware to be updated, and allows reprogramming and replacing of their sound files.)

If you are programming through the Digitax system itself, via a separate programming track, each decoder CV setting you need to change will need set individually. (Unless you are not changing it from factory default. Most settings do not get adjusted in most cases.) Most commonly changed are DCC Address (2 or 4 digits, except 00 and 03, most use the locomotive road number, in your case 2576), Start voltage (recommend 1 on this unit, then adjusting up if needed until slow smooth start on throttle step 1.) and momentum. Lighting settings also could be adjusted. (I believe this locomotive has lighted ditch lights? If so, and they have separate wires {F5 and F6 on the circuit board}, they can be programmed to alternately flash, like the prototype does, when DCC Function 2 is pressed. {Horn on Sound decoders.} They then will continue to flash for a set period (generally 5-6 seconds) before going back to solid.)

Programming on the main does work on most settings, but is more difficult. (Can be done. Just a pain in the behind.) If programming on the main via OPS programming, the only locomotive on the rails should be this one. (Separate programming tracks make this easier, as then you know exactly what locomotive is being programmed.)

They (Bachmann) did just release the newest Amtrak diesels, DCC & Sound.
Many other DCC with and without Sound Amtrak and CSX units are also available, through various manufacturers. (Atlas, Athearn, Intermountain, ScaleTrains, Walthers, Bachmann, Rapido, and others I may have missed.)

And if "DCC Ready" has a plug, it is simply plug in the decoder. No soldering of any wires needed.
(Unless you are installing sound - Then you need to solder the speaker wires. Or extra lighting functions beyond the standard ones...)
Newer (last several years in fact) DCC Ready are equipped with a quick plug, either 8 or 21 pin. Simply remove the body shell, remove the dummy plug for DC operation, and plug in the decoder.

With a couple of the Digitrax systems, you can run 1 DC loco with address 00, but it is rough on the motors. I really recommend not running DC only on DCC.

I am going to start off by saying I am very well aware that the gears inside the Bachmann Climax have issues. (They should not, but they do...)

However - I was under the impression it was the gears in the trucks, not the gearbox itself.
The cylinders spin, but zero driveshaft movement at all. I have pulled off the ash-pan, but all the gears I could see without further disassembly appear ok, with no slipping detected.

Is this also a "known issue" with these models?
Is mine a fluke?

Is this something Bachmann could fix, though OOW, for the standard fee?
Is my getting it from a vendor at a train show, as NOS, going to affect the repair, as there is no receipt? (This vendor, you pay cash, you do not get a receipt to speak of... But you get a better price with cash...)

I am confident I could have replaced the truck gears if they cracked on me, but higher up in the gearbox?? Not so confident....
Could there be something I am missing? I only attacked it from below, as that was the easiest to get to based on the schematics... How would I get at the top of the gearbox?

If it was the top of the gearbox, would the cylinders still spin?

I am sure it is not a lubrication issue, as the factory lubrication on this one is very heavy, to the point of being everywhere and needing much of it removed.

Appreciate any and all help provided.