Instructions
Unplug all cables, including the A/V cable. Inspect each cable and connection point for damage or obstruction. Once complete, securely reconnect all cables.
Plug your Xbox 360 into another electrical outlet, as the problem may actually be resulting from a defective power outlet.
Press the eject button, as this is an alternate way to turn on the Xbox 360. You may find that the power button is not responding. If this is the case, your faceplate is probably positioned wrong and needs to be removed and put back on properly.
Check the light on your power supply. If the light is green or orange and your Xbox 360 is unresponsive, then the unit needs to be sent in for repair. If the light is red, however, then the power supply may have overheated. Let the unit cool down for half an hour before turning it back on.