I have a Mid 2011 27 inch iMac - i7 that died one day. After looking here for answers I replaced the power supply like most posts recommend. (I had one LED test light lit) No joy.
I was headed to swap out the logic board when I decided to unplug the video card and try to boot the computer. It beeped at me and I got two test LDS’s lit. I tried baking the video board, no change.
I then found a new video card on amazon and ordered that. Bing! Back in business! :)
I thought this info might help someone with the same symptoms avoid buying the wrong part.