Sadly the GPU board has failed ;-{
[https://www.ifixit.com/Store/Mac/iMac-27%22-EMC-2429/Graphics_Cards|iMac Intel 27" EMC 2429 (Mid 2011) Graphics Cards]
We don’t have guide you can follow directly, but this one will get you mostly there [guide|7575] Then finish removing the cables so you can remove the logic board fully on the back side is where the GPU board is located. Some people find baking it will revive it for a bit other wise its going to take a bit of hunting to find a good one.