$400 isn't much to work with I would recommend building a computer that can be easily upgraded as you get more money.
I would agree and get a dual core cpu, you could try and overclocking for a few faster mhz.
When you buy ram I doubt you'll be able to afford 1 gig or ram. So check how many slots you have on your motherboard plus if its dual channel ram. I would buy like 512 than later upgrade to 1 gig. Well then again I'm not too sure about building budget computers.
Dont forget OS unless using old, this adds up. If you really need to you dont need a case, yay better ventilation just make a makeshift one. But be sure not to smash your parts to bits... I would recommend buying OEM's as there are much cheaper but only come with limited manufacturers warrentys.
Yeah, $400's limited, but there is a shortcut: jack as many pieces as you can from the pc before it. The one I'm on cost me aorund $450, but it uses the hard drive, dvd-rw, fan, keyboard, mouse, stereo, and monitor as the pc before it.
And with some luck on newegg's sales week, lol - dual core 3.0ghz amd athlon x2, 2gb ram, 512mb video card, and a $20 psu to run it all.
It's possible to build a computer from scratch on $400 too - just don't plan on it doing much when it's done, cause frankly you put $20 into a case (plus $20 s&h), $20 into a dvd burner, $20 into a cheap keyboard/mouse combo, and $20 into a PSU and you've already sapped $100 of the $300 without actually buying any of the guts.
Jack what you can that works; you can always upgrade stuff like a drive later.
And one tip with the OEM suggestion - make sure you've got the cables to run the stuff (ex: have a sata cable for the sata drive or an IDE cable for any IDE drives - some motherboards come with some, others don't. OEM's don't come with anything other than the drive itself - no cables, no manual, no fancy box in many cases)
EDIT: And for gods sakes google for reviews. Otherwise you'll buy boards like the one in mine; after I searched it I found the onboard lan failure rate is about half and half. Seems I'm on the bad half - had to buy a $30 wifi adapter cause it's a royal pain in the backside to replace a bad motherboard.