$800 for a gaming system is quite a lot these days...
If your MoBo (mother board) is equiped with an AM2+ socket, you could just upgrade the CPU and get a beefier GPU and save A LOT of money.
Could you get the exact model of your MoBo? Maybe you don't need a whole new system at all. The Core i7 upgrade sounds cool, but for what you list, is kinda overpriced IMO.
Oh, and the 320MB of the 8800GTS is the factor that tells me it's going to perform under the 6570 in all scenarios, but don't have proof of it; just intuition, lol. Remember the 320 was very handicapped in both memory and gpu power. If it was a 512MB 8800GTS/GT it would be a different story.