Same problem for me too.
Macbook Pro 15 Early-2011
SN: ends with F91
AMD Radeon HD 6750M 1024 MB Graphics
Manifests as red-horizontal lines at boot. Once OSX attempts to do something with the AMD GPU the screen goes gray and nothing else happens.
Using the CMD-S and root commands shown here: http://www.mactrast.com/2013/10/owners-early-2011-macbook-pro/
I was able to get far enough to log in and get a TimeMachine back-up. I did this though while the screen was still having some odd lines and then a sync issue where the screen is moved to the right six inches and then over-writes and reappears on the left of the screen.
I am not interested in buying a new $2800US current generation Macbook Pro after this $3000US machine failed after less than three years.
I am also not looking forward to being told that I am out of warranty, there isn't an acknowledgement of the issue and an agreement by Apple to fix it, and that I'll need a new-to-me logic board that is likely a refurbished unit for between $500-$1000US that only gets 90-day warranty too.
Angry owner of: Macbook Pro 15 Early 2011, Macbook Pro 13 Late 2011, iPad 2nd gen, iPhone 4s, iPhone 4, iPhone 3g, iPod.
Apple please stand by your products.