My key fob doesn't work any more. I have replaced the battery but it didn't help. Just the Panic button works but no others. When I buy a replacement do all the numbers need to match up.

GM/UTA 25628814
FCC ID: KOBUT1BT
CANADA: 1983 101 393

What is the most important number here? I have found some that the GM/UTA numbers match up but none of the others and I have found some that the FCC ID and Canada number matches up but not the GM/UTA.

Well, I'm not sure which of the numbers is most important--someone else may be able to better answer that.
I can tell you this though:
My 96 SSE came with 2 remotes, both of which worked just fine (I upgraded to a remote start/keyless entry system)
Both of the remotes have the same FCC number (K0BUT1BT), but have different GM/UTA numbers (25668603 & 25678792)

If you find that only the FCC number has to match, and are interested in them, shoot me an offer

As long as at least one button is recognized by the car, then yes, the other buttons on the key fob are probably dead (i.e. the problem'* in the key fob, not the car). But can you carefully take it apart for a look-see? I had to do this on a few of them over the years. The usual problem is that either the flexible button cover gets a little out of position over the contacts, or the contacts themselves just get dirty.

If you've seen the price of replacement transmitters you know you have nothing to lose by trying to clean yours instead. I'd try a little rubbing alcohol on the little carbon-button/circuit-board contacts, or a clean pencil eraser on any brass or copper, metal contacts.

I personaly like keylessride.com for replacements, but I know gmpartsdirect is cheaper. Keylessride comes with directions and a tech number, and you don't have to know the exact part numbers.

I was thinking more like ebay. I did get my fob to work I opened up cleaned it and had to solder back a spot but it works. I am still going to try and get another on though.

Another idea is to go around some of the local store and check their lost and found. How will they know they don't belong to me. Most of the time they will just give you a big bucket and let you look through them. I work at a local walmart and we probably have 100 sets of keys, I don't know why we don't throw any of them out, some have been in there awhile.

Also if you could find a remote with all the numbers matching would it work without reprogramming the car or is it still going to be necessary.

If I'm not mistaken you'll still need to reprogram the car because each transmitter has a unique RF signal.

Right; the car is programmed to learn the remote(*), not the other way around. Instructions for that are in the TechInfo section.