What parts do you have?
Finding legacy parts is going to be pricey.
If you're starting with an empty case, you're going to get away a lot cheaper building something more recent than a Pentium 4. You're better off buying something that is actually running or may need some TLC from e-bay or craigs list.
I could put together a spare tower with spare drives/cables and video card that is a 2+ GHz dual core and 2 GB of RAM for under $200. If your budget is under that... Well, I found a Pentium 4 tower complete on the side of the road one day. Booted into safe mode and the drive was 100%.
Edit:
malachi, I gave a few options that are probably much cheaper than 2 GB of DDR 400 new. And the e-bay market can also be a pain...especially since it's so easy to get burned. Maybe you're too good to stop on the side of the road and pick up a tower for parts? I also forgot to mention that one of my twin 19" CRTs was $5 at a garage sale and one of my hard drives I picked up for $4 at a salvation army (it was still sealed in it's anti-static). Point is that I wouldn't trust e-bay for picking up such older components and with shipping, it's not worth it in my opinion if you can deal with someone locally. Or get your parts for free...
If you weren't talking about me (not sure how you couldn't with two other answers and you using the plural...) then I apologize.
Edit 2:
You could always put an ad on Craigs List that you will pick up and recycle old computers for free and remove it (the ad) after a couple of leads. Then go pick up the computers, strip them and recycle what you don't want to keep (I'm not advocating fraud here to save a couple of $$). If you don't get everything you need, put the ad back up...
PS if you're going to be looking at older motherboards, I recommend you visit this site:
http://www.badcaps.org
That site saved my socket 939 motherboard... Which is good since I have 2 processors and it's an obsolete model with no comparable replacement. I was able to successfully replace the capacitors on my motherboard and it's been running great for over a year now, even through some overclocking fun...
_