Either one, and you should test both the extra monitor and graphic card.
Actually test out the extra monitor first. At least if that was the problem, you wouldn't had to have gone through the trouble of swapping out the graphic cards.
I have a 5750 but had the EXACT SAME problem, thing is I only have the one hdmi port, how did you fix it? I'd love any insight/help I'm at my wits end.