Sounds like a short in the computer drawing too much from the power supply and causing it to shut down. If you have a multimeter, try comparing the resistance readings between the power supply voltage lines and ground... and each other... to a known good machine.
I once saw a 2000 fried by a lightning strike on the phone line.... took out the modem, Paula, and shorted the serial port driver chip. That last kept the machine from powering on.
-Jim
