I am having the same problem out of nowhere. Since I have owned my Xbox 360 (4 years) I have never connected to the Internet once; so I do not think it has anything to do with Microsoft. Also, I have two sets of AV cables for my 360 and tested using both cables on two different TV's with same results. Sound works perfectly fine, but I get absolutely no video.
I was playing a game and my Xbox 360 was working fine, then I swapped games and the console's load screen started showing patches of green (which I had never seen before) and then the game's load screen kept going from normal to a green screen. I thought it was the game messing up, so I put back in the original game I was playing and I got a black screen. I tried a bunch of different games and DVD's and I cannot get any video.
I am thinking that maybe the GPU went bad? Any advice is greatly appreciated.