You can probably get better performance for cheaper by getting a new system - you'll be able to buy the FAR cheaper DDR 3 ram, and a Pentium for $90 is more powerful than a core 2 duo by a significant amount... and the motherboard can be found for perhaps $80.
You should be able to fit in the 6570 and The CPU since the motherboard supports socket 775 and it has a PCI ex 16 slot.
Still, you're going to have to get DDR2 Ram/Memory since your motherboard can't support it. And just to be sure, this is your motherboard correct?
Just make sure that's the motherboard you have.
And for the Ram, DDR2 memory are more expensive then DDR3 due to them being older, it'd be better if you upgrade into a new system but you can find ddr2 memory but it'll just be more expensive. Hope this helps!