None of your suggested diagnostics have helped me get the computer
working :-( At this point it looks like I'll be upgrading a bit ahead
of schedule. Here's the tentative parts list (from NewEgg):

EPoX EP-9NPAJ Socket 939 NVIDIA nForce4-4X ATX AMD Motherboard - Retail
Model #: EP-9NPAJ $88.99

MSI NX6800-TD128E Geforce 6800 128MB DDR PCI Express x16 Video Card -
Retail
Model #: NX6800-TD128E $194.00

AMD Athlon 64 3500+ Venice 1GHz FSB Socket 939 Processor Model
ADA3500BPBOX - Retail
Model #: ADA3500BPBOX $219.00

I'm just looking for suggestions, like if I can get something else with
the same performance for a lower price, or if an upgrade that doesn't
cost a lot is worth it, etc.

Also, I notice that the mobo says it uses DDR Standard DDR 400 (PC
3200). The memory I currently have is DDR 333. Will it still work in
the mobo or will I have to get new memory too?

Ugh, this is all looking very expensive.

Also, if anyone has any suggestions on overclocking options, I'm
receptive to those. Can I safely overclock the CPU and GPU? What
aftermarket coolers would you recommend? Thanks!