I'm assuming that you have a large tower case. There are different models to that PC.
The computer uses an LGA775 socket and has 1 PCIe x16 slot and a 300W PSU.
The most powerful GPU that will fit in there and run is the GTX 750ti. It draws all of it's power (up to 65W or so) from the motherboard and the PSU has enough, although it may be old and starting to degrade, but there's no easy way for us to know.
Posting a good photo of the back of the case would help. use a host site like tinypic and cut and paste the bulletin board code it produces.
There are many lesser GPUs that are cheaper, that will work, such as the GTX 730.