I think you can assume he is not a programmer or dealer. He wants to just swap internals to get a working combination. The responses here have ignored that question.

So on that note, I will say that ive never opened a ML-600 up, but I am thinking the pad underneath the volume button has possibly gotten dirty. I think it may have just a contact pad on it that the button hits. Ive seen them get dirty on many types of remotes with those rubber buttons. I'd pull it apart and try and clean it. As far as swapping parts, it depends if the board with the contacts is separate from the memory chips.

Its the rubber membrane or key pad that has lost conductivity, switch out the key pads and you'll have new remote. Leaving alone the original programming. There are other remotes with same key pad, they include mx-700, mx-800, mx-850, and the mx-650.

Thanks everyone! I am going to try swapping out the rubber membrane and key pad (cannibalized from another remote). Is there any trick to opening up the case on the ML-600?

Thanks to the wonders of the internet, I just found a video with instructions on opening the case:

Well, I have the answer to the question that no one was asking but me, and I figured I’d post it in case it helps anyone out down the road.  Yes, you can replace the touch layer underneath the buttons on a Crestron ML-600 remote without replacing the motherboard. 
 
After you get the remote open and remove the 4 small screws holding the motherboard to the front case, you can access the touch layer.  It is the salmon-colored film in this photo:

 
The touch layer is magnetically affixed to the motherboard.  Here is a photo of the motherboard with the touch layer removed:

 
This means you can easily remove the nonfunctioning touch later and replace it with a functioning touch layer from another remote, which is what I did.  I bought an Aeros MX-850 on eBay for about $50, pulled out the touch layer and used it to replace the touch layer in my Crestron ML-600.  No soldering required.
 
If anyone is interested, the only difference between the two remotes seems to be the wireless radio.  Here are photos of the back of the Crestron ML-600 motherboard (showing the external antenna):


and the back of the MX-850 mobo (antenna not attached):


You will see that the Crestron antenna attaches using a multi-pin male/female adapter in the upper-right corner, while the Aeros attaches differently (couldn’t immediately see how, but I didn’t care since I’m not trying to use the Aeros remote).
 
Thanks to everyone for their help!

That salmon colored film is not what you think it is, all that is for is the backlighting. It could be completely removed and remote would still work, of course without backlighting.

On your mx-850, where the missing RF circuitry goes, see the mylar for the lcd screen, between the flash or room lighting shadows streaks, just to the right is where it is soldered.

Got it. So what fixed the remote was replacing the rubber buttons, not the salmon-colored film. Either way, I'm just glad my volume button works!

Yes, that's about it.

So, can you take an mx-850 remote to replace the outer casing of an ML600 remote as well as the rubber buttons?... I have to replace a very used ML600 that still works well but is held by tape and looks worn out.

Thanks for all the very helpful info here. It is very much appreciated!

Sure, they would work.