No, the processor you want, the G645 is NOT compatible.
At the moment you have a very poor CPU, and you definitely need an upgrade if you plan on playing games. Unfortunately the processor your want, the G645 is not compatible with your motherboard. So you're going to need to look for another CPU, personally I would recommend at Core 2 Quad (as they are still considered to be high-end, according to benchmarks). Regardless any new CPU you purchase will most likely be better than your current CPU.
All your motherboard compatible processors are listed here:
http://www.biostar.com.tw/app/en/mb/introduction.php?S_ID=518#cpu
If you can afford, the Q9550 is one of the best (not the best, but one of them) CPUs you can take; it's a Intel Core 2 Quad and is a high-end processor. However if you want the cheapest Core 2 Quad your motherboard can take, it's the Q8200; which is still a great processor, and better than my current Sandy Bridge Pentium Dual Core. If you get the cheapest Core 2 Quad compatible with your motherboard, the Q8200, you'll still be able to play most of the games out there.
All the best.