|Most likely you have a hardware failure in the PSU, motherboard, cpu or a combination of those three so no reset is possible.|
However perhaps one of the peripherial items has failed--one of the plug-in cards or one of the drives. Temporarily remove all the cards except video and disconnect all the drives. Then boot up and see if you get a posting screen. Or, if you were inside the case fiddling around maybe it happened then. I just assumed that it was due to the power failure since that's the only thing you mentioned.
If you get a posting screen then one of the items you removed is the cause. If you don't get a posting screen then you're back to the PSU, motherboard or cpu. Most of the time the PSU is easiest to test by swapping it with another one.
If a different power supply doesn't work then you probably should look to replace the motherboard. If so, post back the model number and we can look around for a replacement. Replacing a P-II/III motherboard shouldn't be expensive.