Hmm... that's very weird. That computer never gave me a lick of trouble. In fact, I used it quite often and left it on for days. Did you try reseating the CPU card? I would do that and check the memory. I also read somewhere that a bad PRAM battery can cause weird things with these as well. I'd unplug the PRAM battery and see what it does.

EDIT - Here's a good post on the battery issue -

http://forums.macrumors.com/archive/index.php/t-87966.html