1) Disconnect the power cord from the back of the computer & open up the case.
2) Wear an anti-static bacnd or at very least discharge your static by touching a metal surface
3) Disconnect the main 20pin ATX power connector from the motherboard & the square 4pin ATX2 power connector
4) Remove any PCI cards you have & disconnect ALL drive cabling from the MOTHERBOARD. Also disconnect any internal USB fly leads from the motherboard.
5) You should now have ONLY the cpu+heatsink/fan, memory & video card installed. Locate the round silver battery in the bottom right corner of the board. Just below it, you'll see a plastic jumper cap. This cap should be covering 2 pins (pins 1 + 2) with pin 3 bare. It will be marked JP1. Move the jumper to cover pins 2-3 instead. Leave in this position for about 30 seconds, then return the jumper to its original position (pins 1-2).
6) Reconnect the square 4pin ATX2 power connector & the main 20 pin ATX power connector. Make sure that the case speaker or buzzer is connected also.
7) Make sure the only external devices connected are the keyboard/mouse & monitor. Reconnect the power lead & power on the system
Let me know what happens. i.e do you hear any beeps? Does the power stay on this time? Do the keyboard lights flash up once?