Is the $1000 budget including the components you've already got? If so then the total is about $903. Which leaves plenty to get an AM3 board, DDR3 RAM and a 5770, which while not the most desirable for that res is certainly better than the 5750. Perhaps another forum member will know how to get a 5850 into this budget.
One of the ways that you might be able to squeeze a better card in is if you change the CPU to a tri-core (Athlon II X3 435/440), if you're going to play GTA IV and it is a high priority you will need a quad core,
If you change the card to the 5770 and get the Asus M4A79TD Evo and CPU Combo I make the build to be $957, or $663 if you don't include the components you already bought.
With my suggested board the second slot is actually fast enough to make crossfiring worthwhile, whereas on the board you originally thought of only has one PCI-E slot above x4 speed. x8 is the minimum for worthwhile graphics performance in modern cards/systems.
Wow, thanks a lot, I didn't know I had so much left over in my budget for all those upgrades! BTW I meant $1000 with components I already bought, so this is perfect! Is an HD 5770 not a good card? It won't do very well on 1920 x 1080?
Well according to some on here it struggles in DX11 games at that res. What they mean by struggle I don't know, but I assume that you can overcome any problems by lowering some of the settings. Or by buying another one. Which will beat a single 5850, which is undoubtedly a good card.