Hey, so I just had a gander at your motherboard... which turns out to be an
ECS MCP61PM-HM. Processor socket is AM2+ so you could put a phenom II in it later on which is not too bad of a processor (meaning its still worth it to spend money on the system)
One thing to consider is the powersupply is probably the cheapest cheap garbage that the company could put in. Something could be partially broken in it and causing only the videocard to flake/burn out. It would probably be worth it to open up the powersupply and see if there is anything obviously wrong inside (burnt resister, leaking capacitor... etc).
Current videocard is...
GeForce 8500GT
256 MB GDDR2 memory
I/O Ports: HDMI, dual-link DVI , S-video
http://www.videocardbenchmark.net/video_lookup.php?gpu=GeForce+8500+GT
http://www.videocardbenchmark.net/video_lookup.php?gpu=Radeon+HD+6670
So the 6670 will be many times over better than current... though since your current isn't working it will be infinitely better (heh)
Edit
Was not paying attention, but evidently the motherboard has a built in video card as well as the 8500GT... The
nVidia GeForce 6150SE which is quite a bit worse yet(performance wise). But.. you might be able to function with it if money is extremely tight. According to the website you will need to unplug the existing videocard to get it to work(?)
Cheers