May i ask if your console in the xbox 360 slim, if it is the slim try checking the power on area and button sensor for debris or any other obstruction that may cause this.
Aslo try a another AC power cord If you do not have one, take it to a Gamestop and ask to barrow theres to test the power supply. First check your Power cord connections to make sure there is no lose wire ends and the AC plug is firmly in place on
the back of your console and not lose.
But i recommend you contact xbox customer support at 1-(800)-4MY-XBOX FOR MORE HELP. And it may still be under warranty as well.
Hope this helps in some way.
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