IF you turn on your Xbox360, wrap it TIGHTLY in a dry towel for 20 minutes, then shut it off and turn it back on about 5-10 minutes later, you will be able to play your 360. This is a very temporary fix and can actually void the warranty and cause more damage to your 360.

I tried it the last time my 360 broke down and it actually worked! I got 3 or 4 more days out of it before I shipped it off to Texas to get repaired. It was a gamble though.