I would personally just build a new one, but if you want to budget it, you could swap out some parts if everything isn't integrated. Surprisingly, the game only requires 2 gigs of ram, and a 2.4 ghz dual core. So what's slowing you down could be the graphics. If you have an open pci slot I would recommend getting a GTX 750 ti, which runs for about 129.99, though I have seen it go as low as 99.99. I have also seen videos of people putting one into a prebuilt computer.
Hope that helps.