I have a iMac 2011 and my Radeon 6970 card give up on me. I could not boot the iMac. One way to recover files is to use Target disk mode: Just hold down T on the keyboard and then use a Firewire cable to connect to another mac. Once in target disk mode you can get the iMac to to boot by disabling the GPU kernel extensions(moving Macintosh HD/System/Library/Extensions/AMD* (any file with AMD) to a new folder. The graphics are slow with green vertical lines but better than just a gray screen) .
Note if you update your OS it will reinstall the GPU kernel extensions and it will not boot again.
Non baking method:
Ok I have read about baking the GPU and i didn't want to go through the hassle of taking the GPU out of the iMac. So when your iMac is "stuck" in the boot up mode this is what I did. Lay the iMac down screen side down and wrap in a blanket and block all the air vents with a blanket. The idea is to heat your iMac up so hot that it shuts off. I did this overnight and the next morning the iMac was still on (an hot). It did not go through the auto shut off, so I unplugged the cord and let sit for about 1 hour to bring back to room temperature. Stood the iMac upright and then plugged in and started and, voila! the iMac booted up and the GPU was working fine.
I recommend smcfan control : http://download.cnet.com/smcFanControl/3000-18487_4-102230.html
and keep your fans running at full speed all the time. I also have my iMac tilted downwards as I believe part of the GPU failure is because of the GPU chip heating up and falling out of the socket. So by having the screen tilted down it is using gravity to keep the chip on the board.
Cheers!
ian