Holding the power switch won't keep it on. It just completes a circuit. If anything, holding it for 4 seconds will actually initiate a shutdpwn. It sounds to me more like your power supply is faulty. The 3 and 5V rails may be good, but the 12 volt one may be dead. I had that happen to me on a Xeon PC rig. I had partial power to the motherboard, (NIC RAM and AGP LEDs would light) but no 12v power to the CPUs.