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.