biglaff :
hang-the-9 :
What is the power supply wattage? With that small of a case you will have issues with many video cards due to heat. A Radeon low profile 7750 may work in there with the stock components though, it actually uses less power than a 6670 by about 10 watts.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814202002
It is only 220w .... but I can not find a replacement that is that small. Here is the part number on the power supply LiteOn PS-5221-06. I guess it is very small to fit inside the slim profile case.
LiteOn is a pretty good brand, here is what you can try. A 7750 at full power in a benchmark in a gaming system drew about 200 watts total. This is for a system with a CPU and other components more power hungry than yours. You can get a low profile 7750, see if it will work, it may. I'd say 60% chance. I think the card itself will draw 55 watts at full power.
If it does not work, keep the card and get a larger case and power supply, move your stuff over to that case, or just buy a used computer for $150 with everything ready to go, and install your new vide card. A Dell XPS or Lenovo ThinkCenter tower will have plenty of size and power to run tha card.