What could be wrong especially after a power outage:
1. Power Supply
2. Video Card
In that order. If any of those specific items have been damaged due to a power outage, your computer will fail to even POST.
Something to try if your not weary is to unplug everything, take the side panel off your computer, and take out the RAM and the other removable cards (such as video card, modem.. etc) Sometimes they can store a charge for a short period of time and reseating them can dissipate the leftover charge. The other thing that you can do after is press the power button before you plug all the cords back in. Again, there could be some charge left in the system and pressing the button will help get rid of it.
Once you plug everything in and get it all situated to turn on, press the power button and listen for any beeps and look to see if any of the lights come on. Like mentioned earlier, check to see if you can press the CAPS LOCK and get any lights on or off.
If nothing happens at all, it probably is your power supply, and depending on the model, it could be between 30-50 dollars for a worthwhile replacement, granted that you can replace it yourself.
If you hear a string of beeps, let us know how many, depending on the motherboard, you can easily find out what is wrong from a set of beep codes.