I have a ASRock M3A770DE and two Sapphire Xtreme 5830.
Hey, I have the same motherboard and only one Sapphire Xtreme 5830
My problem might have something to do with yours.
When I go to hibernate, and then turn on my computer again to resume - the fan on my 5830 starts spinning at full speed and I don't even get a picture on the screen, ahd there are 2 beeps followed by 8 beeps from the PC speaker.
I've tried it on another M3A770DE (friend's) and the same happens there.
Could you please try hibernate with one card to see if you get the same result?
I've tried my 5830 on another motherboard and there the hibernate works with no problems.