Computer Does Not Power Up

by Lew
(US)

Computer Does Not Power Up: After I shut down my computer it would not power up on the next attempt.

Since this event a technician has replaced the power supply,
mother board, and CPU (virtually the whole computer minus the peripherals).

At this point, the computer still does not power up (nothing happens). The power supply LED on the rear of the computer is illuminated.

The technician has given up, though he did think an out-of-box failure on the motherboard is a possibility. I don't want to give up on the computer and am interested to know if you have any suggestions on next steps?