i hate to sound like the typical tech support guy, but here it goes:
please check the back of your computer to see that the power supply is properly plugged in. if your power supply has an on/off switch, please make sure it is in the on position.
if your power supply is modular (the power cables are removable) please make sure the power cables are firmly attached to the supply.
if you are plugging into a power strip, please make sure the power strip is on and plugged into a wall socket with power running to it (too much? im sorry, I'm just trying to cover all bases)
if it is not indeed one of those "duh!" moments and its still not working, the only thing you can do is to plug in and test the system with a power supply you know works.
smell it. does it smell like something just burned up inside it?
a little more information might help determine the issue. what is your system build? whats your power supply wattage? how many +12v rails does it have? are you using a dedicated graphics card that requires additional power from 6 and 8 pin connectors? is it modular? what is the brand?
oh yeah, try this too:
Check to make sure the front panel connectors are properly attached to the correct pins on the motherboard. i've been building systems for 15 years and sometimes i still mix those up if i dont look at the diagram a few times when i use a new or different manufacturer's board.
crap nevermind, realchaos said it all with a link. thats just about anything it could be that isn't hardware failure.