The buttons, when pushed, push a rubber or soft plasic against a contact point on the board. (Yours may not be exactly that but it will be damn close). the rubber starts to break down and leaves a black residue on the circuit board. Take the fob halves apart and spray an electrical cleaner (if you can get your hands on liquid Freon, it's the best as it totally evaporates into the air in a matter of seconds (and goes on to dissolve a whole bunch of the ozone layer). Spray it on the board or on a piece of lint free cloth. wipe the board contacts and the underside of the button pushes with the cloth. Put it back together and if that was the problem, the buttons should work. I do this all the time with my older key fobs, remote controls around the house, stereo components, etc. Works great but I'm down to my last litre of freon.....
@turbozig might have a suggestion on what cleaner to use as they outlawed freon some time ago. Hopefully that is the problem, but it sure sounds like it.