Erg, I used to know the exact fix but it's escaping me right now... it really is a simple soldering job, too...
EDIT: Oh yeah, duh, now I remember. Bad cap on the sound board. IIRC, it was C7. Replace that cap and you're good to go. That's a very common issue with Game Gears. It will take 4 times longer to disassemble/reassemble than it will to replace the cap.