Right, just spoken to my brother.
Is it a launch machine ??? If so, microsoft extended all the 12mths garuntees for another 12mths as a good will gesture. This may also apply to non launch machines but you'd have to ask and see.
Basically he said Microsoft aren't always very forth coming about the extension and might fob you off, so say that you know people who have had their garuntee extended and their machine fixed for free.
He said, before you ring them, make sure you have tried unconnecting everything and trying it again and also if there is a hardrive attatched, remove it and try with out it, because thats what they will ask you to do anyway.
The website is www.xbox.com and the customer service number is 0800 587 1102.
If they agree to repair or replace then they will tell you that they are going to send you a label for you to stick on the box and then UPS will collect. This is crap, they do not send the labels out, and then UPS turn up on your door step the next day to collect the machine. When they do, tell them you haven't recieved the label and I think he said they take it anyway.
It needs to be boxed up well but not in the original xbox box.
Hope that makes some sort of sense and if you need to know anymore, give us a shout and i'll ask my brother again.