Have you found any case where a card that does not work on a 2011 iMac but works on another apparently identical 2011 iMac ?
I'm asking because the friend I bought my 780M from had the very same symptoms as others on this thread with it:
card works fine on windows laptop, but when mounted on his 27'' 2011 iMac, boots without display attached, but after flashing it with linux tool, it no longer boots, just black screen and chime loop.
He lends it to me and I tested on my same board-id and display-id iMac, and to my surprise it works...
It may be a bad install on his iMac, but he tried several times (remounting, three pram resets without card, etc.) and he's very skilled...
Only thing I see different between our machines may be memory and smc firmware version ...