After about 10 minutes the screen goes fuzzy then

This is a common fault with the 360, it says that its a "general hardware failure" which could mean
anything
really. In truth its the lead free solder that cracks with so much heat and as a result the Xbox 360 fails
causing the 3rrod (3 red rings of death) or e74 or even no sound but graphics or sound and no graphics or a fuzzy screen after a short play
just like you are reporting.

Firstly get a spare AV cable from someone else, try this, if that does the same then try a different
SCART
input on the TV. if all this fails you need to fix your machine as it WILL get worse

You will need to get a 3rrod repair kit or get someone to fix it for you, there are guides available on the
internet. I'm in the middle of producing one right now that I will make available free of charge for all fixya
members.
Linda

This is because the soldering is becoming loose between the GPU and the CPU - you need to fix this. You can either do this yourself or you can send it in to Microsoft and they will fix it for you.