Desktop won't boot

Most likely your motherboard is fried. If you don't get a visual at all on your computer than its the motherboard, but if you get a blue screen but won't boot windows than your memory is most likely die. If your motherboard is dead than your processor might be dead as well if it was a power outage. You need to check to see if it the units attached to the motherboard still work If it does than all you need is to replace the motherboard. Depending on what processor you have the motherboard could cost anywhere from 150 to 300 dollars. If the units are not working off the motherboard you are better off buying a new machine.

That's not good. There is probably some kind of damage to the Mother Board.

Open your case up (try not to touch anything inside) and look for distended capacitors.

A capacitor is going to be a cylinder on the Mother Board itself. A distended capacitor is going to be buldged. It will either not be flat on the top or it will be not a smooth cylinder. Imagine a Pop Can that has frozen and exploded, that's what a distended capacitor looks like.

If you don't have any distended capacitors, I would suggest downloading a mother board diagnostic utility, or if you don't feel comfortable doing that (or don't have a second computer) bring it to a repair shop to have it diagnosed.

It could also be a bad power supply, the best way to test this is to bring it to a repair shop. Most places have a tool that tests it, or can test it with a multimeter. Many places won't even charge you for this.