I wold make sure that the power supply is sufficient. Most likely it is a 300W generic power supply, which would most likely be only good enough for a Radeon 5670/6670 (not that that is a bad thing though.
I have one similar to yours, and I replaced the power supply and am running a Nvidia GTS250. The 5670 is probably the highest you could go without a power supply, the 250 is probably the highest before a bottleneck might occur.
Hello I realize this is an old topic and I apologize if it shouldn't be bumped but I have this now ancient computer and was wondering if the cards mentioned are still the best upgrade for the price? Thank you in advance