One thing you didn't mention was have you tried installing a new device or memory to the computer?
It looks as though the power supply is shutting down. The supply is equipped with circuitry that senses if there is too much current being drawn through it's circuits. In an attempt to prevent this from damaging the power supply, the circuit will cause the supply to shutdown. The term "crowbar" was used as an analogy for this operation.
It could indeed be the supply itself but could be any other device connected to the supply via the power cables or the pci connections to the motherboard.
1. Make sure all PCI boards are seated fully. If a board is tilted slightly this might cause this type of symptom.
If that doesn't work,
Start by removing all power connections to the HDD, CD/DVD, floppy.
Remove all cards attached to the mother board.
press the power button - you'll probably get some beeps from the computer because of missing devices such as the video card.
If the fans stay running and there is no shutdown, then the problem is in one of the devices that you have disconnected. If the failure continues, the problem could be the supply or the motherboard itself.
Assuming the system stays up after removal of all the devices,
Start reconnecting the devices one at a time and then try and power on the computer.
If the computer continues to stay on, power off and reconnect the next device.
If reconnecting the next device causes the same symptoms, chances are that item.
To make sure, disconnect the suspected device and power on again.
If you still have other devices disconnected besides the one you suspect, reconnect the rest one at a time to see if the unit stays on. It is possible to have more than one device produce this problem.
Happy troubleshooting