With a solution of 1366 x 768, games focus a little more on your CPU and I believe with the setup that you have a Pentium G620 which is a fine CPU with more power than people intent to believe.
If you for some reason are in Los Angeles, I have a EVGA 440GT 1 GB Memory in a box in my closet, so you can try that out for free and see if that's enough before purchasing anything.