Thanks for the response, NF!
The symptoms are that when the ON button is pressed, a fan starts, lights on the front come on, and then it all shuts down.
I don't know if it's the CPU, but could it come on for even a few seconds and run the fan if the power supply was dead?
There is no fan on the chip, and the power supply doesn't look like it has a fan. (The inside setup is rather elegant... very tidy looking)
I don't remember hearing anything from the hard drive.
At first I thought it might be the switch, but even if I hold the ON button in, it shuts down. The switch is not trivial to get to.
It used to be a UNIX server (now running win 98) and never crashes.
Any ideas?