See what your secondary error code is as rick says. The problem is likely a cold solder joint between either the cpu / gpu, you can try three things to fix that.
Replacing the Xclamps would be the easiest to do at home, however usually consoles that have that done fail again within a couple of months. If you Google you will find many stories from it working for a couple of hours, to a couple of months. Think of it as more of a temp fix.
Good tutorial on that here:
Llamma's Xbox 360 3RLOD (three red light error) X-Clamp Fix
Xclamp Fix:
[video=youtube;uB2QoJM7p5I]https://www.youtube.com/watch?v=uB2QoJM7p5I[/video]
Reflow: The next best fix, the console should be pretty reliable after that.
[video=dailymotion;x7xcuj]http://www.dailymotion.com/video/x7xcuj_xbox-360-bga-reflow_tech[/video]
Reball: Permanent fix by all accounts, pretty extreme but ive heard nothing but good things about it.
[video=youtube;j-8mcJuZOUc]https://www.youtube.com/watch?v=j-8mcJuZOUc[/video]
If you look about on sites like Xbox-Scene many people specialise in doing Reflows / Reballs, you could try the Xclamp fix first, then if the console fails again see if you think its worth paying someone to reflow / reball it.