You press the power button on your CPU, and nothing happens. You press it again. You wait a bit, then press it again. It seems your computer has finally flatlined... or has it? Before scrapping it and heading to PC World, try this technique:
Unplug the power lead from the CPU. Not the plug at the wall, but the thickest plug in the back of the actual computer.
Press the power button on the front of your CPU. Yes, it's ridiculous. It won't power the computer to life, but it apparently resets something in the computer's memory while it is inactive.
Wait 10 seconds.
Plug the power lead back in and press the power switch again.
This technique has worked for me a few times. Let me know if it works for you.