[G4] Another DA G4/466 issue

[Sam]

I acquired a G4/466 Digital Audio PowerMac with initial symptons of simply
shutting down. No warning, no crash, just instant random power-off. Got
worse until it wouldn't power on at all.

I found the power supply fried and thus replaced it, at which time I noticed
the hard drive was also shot. (Symptoms of a power surge, but no surge to my
knowledge.) 

Put another hard drive in, loaded 10.4.4 and it runs well most of the time,
as in idling or running iTunes all day. However, recently when asking a bit
more of the Mac, like surfing in Safari while playing iTunes, the shutdowns
came back. Again - no crash, just an instant power-off.

Reset PRAM, hit the mobo reset switch, reset NVRAM, pretty much all of the
obvious stuff. Did not replace PRAM battery. (does not reset date or
anything after a power-off)

Seems like it somehow overheats and shuts off, but I can't yet confirm;
currently trying it w/ the door open.

Any suggestions? Bad CPU? Bad video card? This one has me puzzled.

-Sam