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 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.

Make sure the motherboard surface is not making contact with the metal case (except at its mounting points). Take the motherboard and power supply out of the case and place them on a non-conductive surface (wooden table, etc.). If it boots, something was probably shorting out in the case.