That's an absolute disgrace. I have a Playstation that I bought in 1997 and still works perfectly fine. But an Xbox 360 with better technology breaks down after a month.
Luckily, this has never happened to me. However, I have heard a solution to this problem. It's called the 'Towel Trick"
Here is the link to the site, just follow the steps:
http://www.squidoo.com/xbox-360-towel-trick-three-red-light-error