You can't do dual graphics with a 6770, they highest it goes is 6670. I would also recommend a 7750, just make sure it uses DDR5 and not DDR3, there's a big difference in performance between the two.
No dual graphics with the 7750 either only a few 6k series cards.
that's what I meant. 6670.
no matter what it doesn't seem the OP has the funds to do it right so I would suggest lowering the resolution and turn back some game settings and live with what you got.