I checked your prices and the cheapest reasonable 1 GB geforce 460 was $170 from MSI, which is $340 for 2 cards. Conversely, the best AMD phenom II x4 for the price is the black edition at $130. So that right there is $470. Now you have $130 for all other parts. This is completely unreasonable for a case, RAM, an HDD, a motherboard and a power supply.
Now realistically, getting 2 460's is pretty cost ineffective. You can get a card that is essentially 2 460's stuck together into one card for $385, but its still not that useful. Getting multiple graphics cards is pretty useless if you're getting the cheapest possible mobo, cpu, and 4GB of RAM, and your computer would honestly be a lot better if you just got 1 card and invested the money into other stuff.
Honestly, $600 is really tough to hit for a gaming computer, and basically I managed to hit $870 with the flexibility to work down. It would REALLY work out if you could somehow reuse your old HDD and case (which would bring you down to $710, and from there you could cut the ram from 8GB to 4GB to save $25 or maybe get a slightly lower end mobo for saving $40. If you did that, you would be down to $655, which is slightly over, but I'm guessing is doable.
If you want some help, go ahead and PM me or something and I'll help you out.
Props to Greekgeeker for helping me out work out this build.