Instructions
Check to ensure the power supply is plugged into an electrical outlet. If it is and the Xbox power supply is still not working, try a different outlet.
Unplug the power cord from the wall outlet and the Xbox 360 power supply. Examine the cord for damage; if none is present plug it back into the power supply and wall outlet.
Use a different power supply and power cord on your Xbox 360. If the system powers on, your other power cord and supply are faulty and can be replaced by contacting Microsoft support. If the system still does not power on, there may be an issue with your Xbox 360. See Resources for the contact information for Xbox support.