^don't listen to him, he's new, doesn't play modern games and doesn't know jack. I'm cool because I do know jack, he's pretty swell... until he lost his arm in the war. Now he's one arm creepy jack who scares kids at local parks with the "pull my arm" jokes... He uses blood die packs for special effects... Its kinda cool if it wasn't so damn sad... Still I laugh my ass off.
Anyhow, you have a decent video card, but as you know, its not paired with a modern cpu to take full advantage of it. Your cpu is holding your GPU back a lot by as much as 50%. When I jumped from my e8400 to an i7, my 5870 gained 120% in frames just from the faster cpu and memory in modern games like BC2 at the time. Your GTX 560 should have be able to play most games at medium/high at 1080p with AA pre and post off.
However you can bring new life to your cpu by overclocking the crap out of it and bring that power up to par with current low end modern cpu's, without much money. At stock, you should be getting around 25 GFlops, an stock i3 dual core nets around 32-35 GFlops. Adding a cheap Cooler Master 212+ cpu cooler should net you around 3Ghz or possibly 3.2, depending on a few other factors and settings. Although, you are running an Intel DG and if my memory serves me right, that doesn't allow overclock... nevermind...
Ok, start from scratch.
Mobo:
Asus P8Z68-V LE $140
CPU:
i5 2500k quad core $224.99
RAM:
Kingston HyperX 8gb (2x4) DDR3 1600 cas9 1.65v $46.74
Total: $411.73
With a few bucks left, you can throw in a
Cooler Master 212+ cpu cooler for $30 for a little overclocking headroom and spend the rest on games...