For gaming at least a quad core CPU is recommended. If I were you I would build a new system ground up since your hardware is all dated. Also look at the benchmarks for video cards at different resolutions.
If you upgrade your video card, your CPU would be the bottleneck but your FPS should still increase a bit. Do NOT get the 6770 as it is essentially the same as 5770 with minor bios tweaks. Get HD 6790 or an Nvidia card.