Chosen Solution
My mid 2011 27 inch iMac had GPU problems which I solved with oven baking the card but came back three months later. I opted to buy a replacement GPU purchasing a 109-C29657-10. I noticed some small differences with the text on the card but I figured that was a newer revision of the card. Installation went well but after reassembly my iMac fails to stay powered long enough to boot to macOS. If I boot into recovery mode it can stay on for hours but the moment I try to boot into macOS it power cycles. I have taken it apart and put it back together multiple times. I am at a loss. Any help is appreciated thank you! Update: Sadly purchased a bad GPU off ebay. Resorted to re-baking my old one and it fixed it for now.
Sadly, I think you got stuck with another bad GPU board ;-{ The problem is two fold… The parts being sold are used boards as the MXM boards are no-longer being made and many are not the Apple version of the board! Apple altered the boards firmware so your system won’t boot up properly within the OS, and as you noted it appears to work just fine in Safe Mode or in Target Disk Mode as both use the Intel graphics services within the CPU chip, bypassing the AMD GPU logic. So we can glean from that the board is not shorted out which is what I often see. So you risk getting a bad board which is quite common as people over stressed this systems graphics and if you do get a good board it still may not work unless you re-burn the boards firmware.