Hey guys - Apple did replace my logic board for free. (Same problem, vertical lines first, then could not boot ... see my earlier post in this thread for details) I booked an appointment at the Apple store nearest to me and showed the problem, along with everything I had tried (I'd spent many many hours so was quite knowledgeable in talking with them) After performing some simple diags, the lady I spoke with disappeared to the back for a bit and came back saying yes, my diagnosis seemed correct, and that it would be $700 plus dollars for a new logic board. I mentioned this thread (gave her the specific URL for it), and that it seemed to be quite a widespread problem (but unlike the 2010 mbp graphics recall was not yet formally acknowledged by Apple), and that it seemed to just depend to whom one spoke as to whether it would be a large, small, or nothing cost to get fixed. I referenced another guy in Australia (which is where I now am) who got his replaced for free also, however note that I used to live in the USA, and my MBP was purchased there. I asked if there was anything else she could do, pointed to the fact that it is in pristine condition and was only just over 2 years old. She said she'd talk to the manager, went to the back again, then came back and said they'd replace it for free. She did seem surprised herself that the manager agreed to replace it since it was out of warranty, but was happy for me, and of-course I was feeling very lucky and loving Apple again hearing that news. They did replace it and it is like new again. I am however concerned about when it will fail again since I do agree that it is a manufacturing issue. I use it mostly with an external monitor (which requires the discreet graphics card - AMD Radeon HD 6490M in my case) and the working temps seem to be approximately 10 degrees celcius higher than if I do not connect the external monitor, and my best guess is that it is indeed the higher operating temperatures for an extended period of time that burns out that discreet graphics card. I think the problems arise depending upon how often and long you tax the discreet graphics card, and possibly also if you were lucky/unlucky with the specific amount of thermal compound was put on your specific graphics card.
On a side note, if I weren't able to get it fixed, I did manage to install Ubuntu 13.04 on it working perfectly, with just the built in intel graphics. If you have no other option, can't get it replaced for free or at a cost you can/want to affort, and want to try that route, I used the information out of help.ubuntu.com/community/MacBookPro8-2/Raring and the "booting from usb pen via efi" to try it out, and then askubuntu.com/questions/149921/how-to-add-a-command-permanently-to-grub2 to make it so I could boot directly from the drive straight into ubuntu. For my early 2011 15inch MBP specifically I added the "outb etc.etc." stuff to /boot/grub/custom.cfg (you'll know what that means if you read the links I just referenced), and then added i915.lvds.channel_mode=2 i915.modeset=1 i915.lvds_use_ssc=0 after "quiet splash" in /etc/default/grub on line GRUB_CMDLINE_LINUX_DEFAULT, and then ran sudo update -grub (which will update the /boot/grub/grub.cfg file for you.)
Best of luck to all.