Here are some things to look for if your PC won't power on:
Check the power cord and outlet.
Check the power supply's connector to the motherboard. Disconnect and reconnect to be sure its firmly connected.
Check the power supply. If you can test it in another PC, try it.
Check the power switch on the PC's case and make sure it's properly connected to the motherboard. Try shorting the jumper pins that the switch uses to power on the PC. If that works, the switch is bad.