Make sure you try swapping in a power cord you know works, just to make sure.

After that, ensure that the connectors from the power supply are securely connected to the motherboard and that the little wire from the from-panel power switch is connected to the correct pins on the motherboard.

If that doesn't resolve the problem, you could try swapping in a different power supply. The problem could also be a bad motherboard, but it's most likely one of the previous things I mentioned.