Welcome back from the dead.
Since you've already got the RAM upgraded to the max, your next best bet is to get a higher end AM3 CPU. If you can, going with an Athlon II would be plenty, the additional cash for the Phenom II wouldn't be worth it for your purpose. The Athlon II X4 640 is a fine chip (Reference:
Newegg.com - AMD Athlon II X4 640 Propus 3.0GHz Socket AM3 95W Quad-Core Desktop Processor ADX640WFGMBOX ) for the money and will easily handle the games you want to play. They also overclock fairly well.
Next, you need to find out what wattage your power supply is. Looking at the specs for the 570 (
http://support.dell.com/support/edocs/systems/insp560mt/en/cs/cs_en.pdf ) it looks like the power supply is a paltry 300 Watts. That'll be OK for a CPU upgrade, but if you want to upgrade the GPU at all, you'll need to get a new power supply as well.
According to some posts I found online in both the Dell community and elsewhere, you can buy a standard ATX power supply to fit into the case - though if you can post pictures of the system to be sure, that never hurts. I did some checking however and we should be OK.
This unit is one of my favorites for inexpensive power upgrades:
Newegg.com - Antec BP550 Plus 550W Continuous Power ATX12V V2.2 80 PLUS Certified Modular Active PFC Power Supply
If you had that, it would significantly open up your GPU upgrade path, and from there, we'd just need to know budget requirements beyond the CPU/PSU to get your video (GPU) upgrade in mind.