Check the light on the power adapter.
Red = Power supply too hot, too much current. Wait for it to cool or try another socket.
Orange = Disconnected or faulty power supply, faulty console. Replace consle or power supply.
Green = Hardware failure. Send console for repair, or buy a new one. That would be cheaper and quicker when it comes to Microsoft and XBOX.
For more info, go to this link:
http://support.microsoft.com/kb/907534/en-us
Hope this helps :)
Carl
July 2009