Check all connectors (unmate them, clean contacts, remate). Carefully inspect the solder joints associated with those connectors.

Carefully look at the electrolytics -- in most cases, you will see telltale smudges where these caps have started to leak. You'll need to clean the board thoroughly and replace the caps (not just the ones with obvious signs of leakage; they'll all need to be replaced). I recommend tantalum caps (these have no liquid electrolyte).

Connector cleaning, resoldering, and recapping generally takes care of the most common problems in these Macs.