My system has a dual-core Athlon and 4G of memory, Win XP. My wife's has a dual-core Pentium, Win 7, and 8 G.
The game runs just fine on both of these.
What motherboard do you have? We could give you more help if we knew. You can download "Belarc Advisor" for free and it will give you complete data on your system, if you don't know.
Newegg has great prices. I updated my motherboard, processor, RAM, and video card for under $250.