You will need to find out what kind of motherboard it is, if you want to change out the processor. Knowing the series of CPU is useful, but you will need more information than that alone. For instance, the Athlon II x2 series of CPU's has 26 different models, and they do not share universal compatibility with motherboards. Also, consideration must be paid to motherboard specifications, some CPU's may physically fit the socket on the motherboard, but the motherboard may not be designed to function properly with that model.
I'm pretty sure your computer has the Athlon II x2 220 2.8GHz processor, and there's a good chance that the motherboard is an Asus M4A78LT-M, but you need to make sure. It is not overly hard to change out a processor, but you will have to do your research.
Aside from this, I'm not convinced that your CPU has died. It could be the motherboard is dead. In which case it benefits you more to buy a new motherboard and CPU combo, or even a whole new computer. What happened to your PC? Does it not power on, or if it does do you just get a black screen? Tell us more about your circumstances.