If it's will my 2ghz core2duo run modern games then the answer is not at any kind of (generally) acceptable FPS,not even if you have a very strong GPU in the system.
What's the question? Gaming with an unknown Dual Core 2.0 GHz CPU and G33 Integrated Graphics? I think you are better with consoles (I don't know which one it is). But if you're going to build a new PC for some dollars, I can help you.