Here you go:
motherboard : MSI K8N Neo4-F
$80
CPU : AMD Athlon 64 3200+
$166
video card: eVGA 6800GS
$209
PSU : OCZ Modstream 450W (with this PSU you can remove the cables you don't need, which will give you better airflow)
$78
RAM : G.SKILL 1GB DDR400 TCCD (not LA)
$152
Total w/ tax, shipping = $761.75
That leaves you enough money to buy pretty much any case you want, within reason. I'm assuming you have a monitor, keyboard, mouse, Windows, etc. since you don't mention the need for them. You're lucky you've got your hard drives already or we'd have to scale some of this back. That's a pretty good system for under a grand. If you're going to overclock, switch the MSI motherboard for
this. That would bring the total to a little over $800, but it'd be worth it, I'm told. The 6800GS is supposed to be able to overclock like crazy. If you want to swing the balance more toward app crunching and away from gaming, switch the 6800GS for an eVGA 6600GT (which has a $20 mail-in rebate right now making the price a crazy $119) and the G.SKILL RAM for Corsair ValueSelect, and then get an AMD Athlon 64
X2 3800+ (instead of the regular 3200+), which is a dual-core processor. The total will be about the same. SLI is a waste of money - do a search here and you'll find all sorts of SLI-bashing.
Yes, the AMD processor will be able to handle heavy apps. Intel has the edge there, but it's not by much at all, just like AMD has the edge in games, but not by much. The main thing AMD has over Intel is price and overclockability, since AMD multipliers aren't locked like Intel. Don't get an Intel dual-core.
Finally, if you can scrape up another $50, get yourself a nice CPU heatsink/fan apparatus, such as the Thermaltake Typhoon (which has been getting a lot of recommendations here as of late) or anything from Zalman. A cool CPU is a happy CPU!