iMac (mid 2011, OS X 10.12) gets stuck on white screen on boot, all DIY options exhausted?

Solution 1:

It's very likely to be the video card. There was a repair extension program (since expired) for the AMD GPUs in 27" 2011 iMacs. They will boot to the Apple logo/progress bar and then hang at a white screen or pink/green lines.

If you're near an Apple Store at all you should take it in or at the very least call Apple and do some troubleshooting. Stores in most of the US (except California, where the timeframe is quite a bit longer) will not carry parts for the 2011 iMacs much longer, likely stopping as soon as a few weeks from now since its been about 5 years since they were discontinued in all markets.