1) Try unpluggig the power cord and let the power supply cool for a moment.
It may be that the internal protection inside the power supply has trigger and it will not reset until it senses that there is no AC power applied to it.
2) Get one of those cheap AT-ATX power supply testers.
They allow you to measure the voltage coming out of the power supply. This is especially critical with ATX power supplies that need to be "primed" by the motherboard.
3) Move the power supply to another PC.
If it can power the other motherboard, the problem is not the PC.
4) Go to minimum configuration
When testing your own motherboard, unplug any PCI or ISA card, including the video card.
Unplug the memory sticks.
Unplug any peripheral conneted to the motherboard.
Make sure to leave the speaker connected, though.
Upon power up, the POST should run and you should hear the speaker beeping.
The maker of your BIOS should be able to provide you with the POST beep codes.
If the speaker does not make any noise, get ready to toss your motherboard.
5) Get a POST card
If you are curious about the nature of this problem, try using a POST card. These cards insert in a PCI or ISA slot and they tell you the status of your motherboard after the POST has run.
One of the best POST cards is the Micro2000, although there are some cheaper ones out there. Google may help you find one.
Good luck!
CBTman