Hands down the oldest part of that system has to be your CPU and MB. If you are going to upgrade, I would upgrade those. I recommend an i5 and a new board.
Next I would get 8 Gb of ram.
That said, I don't know to what degree your CPU is holding back that card. A 7770 is probably a good choice to pair with a CPU that old. Do you have any benchmark numbers. That will let me know how badly the Athlon X2 is holding you back.
Sorry for the delay. The asus 7770 will work fine with the intel MB and CPU so long as the MB has a PCIe x16 slot, and I can't imagine that it wouldn't.
Since your PSU died, another 500-550W will serve you fine with those parts. If you want room to expand to a larger video card in the future, I may go with a 650W instead. The price difference should be small. Seasonic, PC Power and Cooling, and Corsair are all good brands.