Did you connect the 6-prong PCIE power connector to the 5770? The 5670 doesn't need one since it can run off the power supplied by the card slot, but the 5770 needs the auxiliary power connection. It would also cause your mainboard to "beep beep" and the screen to remain dark.
I did connected the 6-pin power connector ..
On other note: If the card is dead which I ll check on other system asap.. So is there any possibility that can it be repaired or not?