Diagnosing a hardware problem can be done very fast if you do it systematically and if you have some replacement parts (which you can easilly borrow from another computer. you don't have to buy them). before you take the following steps disconnect all hard disks, drives and other devices from the motherboard. Leave only video card, ram, mouse and keyboard.
1: The Power supply unit MUST be in good condition otherwise you may never end this diagnosis. The test made for your psu in the lab is not good because it measures volts when there is no load on psu. If you want to make any progress get a known-to-be-good psu, install it and bootup.
2: If the computer doesn't boot with the new psu and you get a beep sound that is ususally a problem with the ram (usually long beeps) or video card (usually short beeps). Take out the ram modules, clean the contacts with a soft cloth, and the slots with a soft brush, reseat firmly and try to reboot. You need only one module for the test but it must be compatible and known to be good. If you still get the long beeps try to move the module into each of the other slots, rebooting after each operation. If you still get the beeps then the motherboard is finished.
3: Replace the video card, preferably with an old, pci card. If it works then either the video card or the AGP slot or the AGP buss are faulty.
4: If still no good take out the cmos battery and use a voltmeter to measure it's voltage. It should be above 3 volts. leave the battery out for about 15 minutes and reinstall. This will clear the cmos settings. Boot up. If you succed in booting you will most probably have to set time and date in the bios to overcome a checksome error message or any other message.
5: If still ill no good then either the motherboard or cpu is faulty. it's more common for the motherboard to fail.