Apologies for bumping up an old thread, but I am having the same issues. I had two 5770s in my Mac Pro, but have sold one and bought a Blackmagic Intensity Pro instead for use within Pro Tools 10.
I downloaded the latest drivers from Blackmagic and installed them and the card. Now when I turn my Mac Pro on, one of the three screens connected to the 5770 won't turn on unless I unplug and replug it. Practically what the OP describes above. When I uninstall the Intensity Pro, everything works fine as normal.
Was there a solution to this? Or does anyone know of one?