No, a 780m die gets hot within the first few seconds it's on. Even though there is no EFI screen. But as it stands, you make it sound like the iMac isn't booting at all. Like there is something wrong with your card, stopping the iMac from booting. The pressure from incorrect thermal pads can bend the card enough to damage it. Which style heatsink do you have.
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When you say it doesn't turn on, do the fans spin for a quarter second and the machine turns off? Makes me think something was shorted on your card. Or the die wasn't making good contact. Pictures please, I've never delt with 6xx card only 7xx cards.
No, it turns on but no chime and fans running at full speed. No image on the internal LCD.
It's very strange, because it worked and then shut down immediately after the login screen...
Tomorrow I will post the pics. I got the 675 instead of the 7xx because the ebay seller has mistaken the model