I have the same issue with my MBP also. I don't know but i see more and more of this issue accruing every time I'm on here. I'm a bit lucky that they are repairing it for free even though i never purchased a Apple Care. hahaha.
Whew lucky me!!
I took this article "Distorted Video or no Video issue"
http://support.apple.com/kb/TS2377 and showed it to a Mac Guises and they were able to honor it. I had to take it to them twice for them to honor it though.
I was a bit disappointed that the first tech didn't offer me this repair when it was available for awhile now. I had to come on here and find that article myself and take it back in the 2nd time, .... this time showing them that same article and they were able to honor it.
I hope to get my back soon. I'm left in the cold without it.
I hope those of you who are going through same thing, ... bring a copy of that article in and hopefully they can get yours fixed also.