It's an old system of mine I haven't used in a few years. It worked fine when I stuck in the closet, but now it's being weird. Sometimes I could make it into Windows but then it'd crash; BSOD. So I threw it back into the closet for another 6 months. Tonight I was looking at it, thinking maybe the capacitors blew. None looked popped as far as I could tell, but I notice the 4-pin power wasn't plugged in. Thinking maybe I had an insufficient power issue earlier, I connected it and booted the system. XP began to load, getting past the boot screen and onto loading Windows. But before it could finish, BSOD. I tried it 3 times and crashed in same place each time. So maybe the install was hosed. I swapped harddrives, nothing. I put the old drive back in, still nothing. Machine won't even POST.

Asus P4P-800E Deluxe
Pentium 4 2.8e (prescott)
2x512GB DDR400 (Crucial I think, copper heat sinks on them)
Gigabyte 128mb GeForce FX5900
Antec 430w psu
no cd-rom is connected right now

I'm cleaning any dust out of the case and reseating everything, but I have a feeling that won't make much difference.

Also wanted to mention, there are no system beeps when I turn it on and no lights flash on the keyboard as it normally would. But the power does come on, fans spin up.

Electrolytic capacitors dry out with old age, they don't blow :)

All PSU's will loose capacity in time due to this fact, even if you stick it in a closet, just not as fast as if it were plugged in and in use (a matter of temperature).
On average, PSU's will loose 10-15% power each year, so your 430W Antec will provide 190W-280W after 5 years

I suspect you PSU is getting too old, and even if the PSU-fan spins up (only 100-250mA), it probably just can't handle the system anymore.

You can try this calculator to see what is recommended as a minimum: