The Xbox 360 may be overheating. See if anything is covering the vents on the Xbox 360 and see if it is in a small area that doesn't allow the heat to escape. If that doesn't work the Xbox 360 may have a different issue. If the Xbox has three flashing red lights around the power button or the power button is not lit up at all try the following:
Solution 1: Unplug and reconnect your power supply.
Here's how:
Disconnect the power cord from the back of your console. Unplug the power cord from the wall outlet and from the power supply unit.
Reconnect the power cord to the console. Then plug the power cord back into the electrical outlet and the power supply unit.
Make sure that all three power supply connections are firmly secured.
Turn on your console, and check the light on your power supply.
If the power supply light is green, check the front of the console to see if it still has three flashing red lights. If the console now has four flashing red lights, attach an Xbox 360 A/V cable to the A/V port on the back of the console.
Solution 2: plugging in the power supply in a different room:
Turn off your console.
Disconnect the power supply from the console and unplug the power supply from the electrical outlet.
Take your console and power supply to another room.
Plug the power supply directly into an electrical outlet. Do not use a surge protector.
Reconnect the power supply to the console.
Make sure that all three power supply connections are firmly secured.
Turn on the console, and check the power supply light.
If the power supply light is green, the problem might be with the electrical outlet that you were using or with your surge proctor if you were using one. Before you plug your console back into its original location, have the outlet inspected or use a different surge protector.
Note If your console displays four flashing red lights after trying this step, attach an Xbox 360 A/V cable to the A/V port on the back of your console.
If the light on the power supply is not lit, this indicates a problem with the Xbox 360 power supply unit. Contact Xbox Support for assistance in replacing the power supply.
If the light on your power supply is still red, please try the next solution.
Solution 3: Cool the power supply
Turn off the console.
Disconnect the power supply from the console and from the electrical outlet.
Plug the power cord back into the console, reconnect the cord to the power supply, and then plug the power cord into a different electrical outlet. Make sure the power supply is positioned so that it gets good ventilation.
Turn on the console, and check the power supply light.
If the light on your power supply is still red, try the next solution.
Solution 4: Request a replacement power supply
If your power supply light is red, the problem is with your power supply Contact Xbox Support to obtain a replacement power supply.
Go here if you need to contact Xbox Support: http://support.xbox.com/en-us/pages/contact-us.aspx