If you had a blackout with the computer on, it's not good for the computer. It could be anything that's not working -- you have to do a process of elimination.
First test the power supply. The easiest is to unplug it from all hardware in the computer, and use a power supply tester
(can be purchased from a local computer shop). Turn on the power supply with the tester connected to the plug that powers the motherboard. Or, if have a comparable ATX power supply (400W or more), then plug that into the computer and see if that works.
If the computer does not post (or give you beeps) after a new power supply, then you have a hardware problem. You could test each piece of hardware in another computer (if one is available).
That would leave the motherboard and processor, if all hardware works. When it comes down to these two, it's a chicken-egg thing. Is it the motherboard not working, the processor or both? Unless you have working motherboard for the Athlon 2600, you could test it on that. Otherwise, you may have to buy a new motherboard and processor just to be sure it works.