For 1600, you could easily build a system around a A64 3700 SanDiego, 1GB corsair ValueSelect, a PCIe 6800GT, and a NF4U based mobo. Those are your core components. The HDD, optical drive, case, and PSU are all relatively easy and cheap. Cases can get really expensive, but I think you looking for something in the economical segment? Said system won't have a Dell 2005FPW LCD or anything of that caliber, but a 19in CRT is easily to fit in that budget. Perhaps a 17in or a 19in LCD, if you shop around and catch some deals.
Building a decent SLI system with 1600 would be a lot tougher, as you would need to spend more on the mobo and PSU, not to mention the two video cards. 6600GT SLI is a total waste, so you'll want to go with 6800GTs/Ultra or 7800GTXs. Two 7800GTXs alone right now will run you over a 1000, two 6800GTs will run around 700ish.