What games are you trying to play?
You actually have the same computer as I modded for my cousin. You have a couple of routes.
If you dont want to change the power supply, you can switch to a Radeon HD7750. Its a good card, but with your budget, you can do better.
For a decent price, you can also get a new power supply and a better graphics card. $200 would buy you a 7950, which would run well on that processor, and is the fastest I would go before I would expect to see a bottleneck. You then can get a new power supply, and with the extra money, you can get a new case to house all of the components.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814131458
http://www.newegg.com/Product/Product.aspx?Item=N82E16814127737
One of those cards would do. They come with free games too.
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139027
This power supply should run the card just fine. If you need to, you could also step up to a CX500.
http://www.newegg.com/Product/Product.aspx?Item=N82E16811129187
You could get a nice case like that too to mount it in, you wouldnt even have to reinstall Windows.
This is pretty much how I built up my cousin's computer. He did it a little differently though.