Instructions
Check the power supply light on the rectangular box in the middle of your power cord. It should be glowing green. If the power supply light is glowing red, try switching to a different power outlet. If the power supply light is now green, the problem was likely with the power outlet or surge protector if you use one.
Cool the Xbox 360 and its power supply. Turn off and unplug the console, and move it to a more ventilated area. Remove any dust from the console and power supply as well. Plug the console and power supply back in.
Request a replacement power supply. If you have tried the previous steps and the console's lights are still flashing red, there may be irreparable damage to the power supply. If your console is still under warranty, you should be able to receive a new power supply free of charge. Contact Xbox support to request that a new power supply be sent to you.