the issue is much more likely down to the video card in that system which is a very old and weak, integrated ATI Radeon HD 3200 which is not designed for gaming in any way. Unfortunately this cannot be upgraded.
I feel a CPU upgrade is a waste in this system because your stuck with integrated graphics. You will need to buy a different computer. No matter what you put into this system for CPU your still limited with the weak GPU.
What games are you trying to play that you need better performance with. Maybe we can make some affordable suggestions.
I have seen people skimp by with Intel Core 2 Duo used system purchases for like $100 refurb with OS included, and throwing the money into a good PSU ( $40-$60 ) and Video Card ($70+ ) instead and able to play modern games pretty well and very affordably on a tight budget.
This gets them gaming for around $250 with ok performance but not a system to brag about.
For around $400 you can start to buy all new guts and have a gaming system, but with a weaker $50 CPU to cut costs etc, but an upgrade path later if you need more performance for number crunching in games.
Buying a used Core 2 Duo system, your only possible upgrade path might be a Core 2 Quad, but you would have to do some research into the system bought to be sure its supported as for not all socket 775 systems can take a quadcore.