70% (or more) of gaming performance is tied to the Graphics card. While Radeon cards generally tax your Power Supply more than GeForce cards do, your card is probably around 20 watts, not much at all(I looked at a HD 4350 as I couldn't find info on 4200). You should check your power supply first, a GTX 960 requires 120 watts, while a 970 requires 150ish.
You should also look into upgrading your RAM. You don't really need as much as 16gb, but I would definitely upgrade to 8.
Your CPU seems decent enough, but I haven't checked any benchmarks. In any case, you can't really upgrade the CPU without upgrading your motherboard as well, at which point you might as well buy a new computer.