Have you done any maintenance such as dusting it out, checking the CPU fans and such?
I've got a Dell PC, with Pentium III, and Windows ME. Recently, my computer sorta shuts down after 15 minutes... The monitor jus goes blank, and shuts off. But the CPU is still on, and the CD drives still respond when I hit eject.
I checked the power settings on my computer and they are all off, i.e the comp is not going into standby or hibernation.
The only way to get it to work once the monitor shuts off is to hit the reset button.