Okay here's my cheap build.
CPU - $64 shipped. Can't go wrong with 2 cores and is cheap!
AMD Athlon 64 X2 4200+ Brisbane 2.2GHz 2 x 512KB L2 Cache Socket AM2 65W Processor - Retail
http://www.newegg.com/Product/Product.aspx?Item=N82E16819103206
Mobo - $66 shipped. Has just about everything including decent onboard GPU. Does okay for light gaming (depending on your definition of light gaming is).
GIGABYTE GA-MA69VM-S2 AM2 AMD 690V Micro ATX AMD Motherboard - Retail
http://www.newegg.com/Product/Product.aspx?Item=N82E16813128043
Memory - $47 - $15 MIR = $32 shipped! One of the cheapest initial cost DDR2 w/a bonus $15 MIR (if you send in for it).
A-DATA 2GB (2 x 1GB) 240-Pin DDR2 SDRAM DDR2 800 (PC2 6400) Dual Channel Kit Desktop Memory - Retail
http://www.newegg.com/Product/Product.aspx?Item=N82E16820211066
Case/PSU combo - $50 shipped!! I've used several of these and have had ZERO problems with them. I've even got a 3850 GPU running on the same PSU (25A on the 12V rail ain't too bad). For a lower powered system this combo is hard to beat.
Athenatech A3603BB.400 Black Steel MicroATX Mini Tower Computer Case 400W Power Supply - Retail
http://www.newegg.com/Product/Product.aspx?Item=N82E16811190072
HD - $50 shipped. Plenty of room for normal use and if they need more than just add another HD later or spend more now.
Western Digital WD1200AAJS 120GB 7200 RPM 8MB Cache SATA 3.0Gb/s Hard Drive - OEM
http://www.newegg.com/Product/Product.aspx?Item=N82E16822136225
DVD Burner - $24 shipped! What else can be said? Cheap and does the job. Will need to get Burning software, if needed, but it has the capability to burn if you need it.
Sony NEC Optiarc Black 20X DVD+R 8X DVD+RW 8X DVD+R DL 20X DVD-R 6X DVD-RW 12X DVD-RAM 16X DVD-ROM 48X CD-R 32X CD-RW 48X CD-ROM IDE 20X DVD±R DVD Burner - OEM
http://www.newegg.com/Product/Product.aspx?Item=N82E16827118003
OS - $90 shipped. Since your on the cheap this will do. Solid and reliable (mostly). Vista still needs some time, if you ask me, but you can get Vista basic for like $5 more, so you can decide.
Microsoft Windows XP Home With SP2B 1 Pack - OEM
http://www.newegg.com/Product/Product.aspx?Item=N82E16832116056
Total ~$389 - $15 MIR = $374 shipped!! Now all you need to add is a monitor. If you want to get a LCD than I'd go to Costco for them. They are generally pretty well priced and they have a good return policy. Otherwise you'll need to watch your ads for better deals or shop online.
Edit: Other options are getting a Dell/HP/Gateway/eMachines pre-built units for about $500 w/17" LCD's. You can decide, but with the pre-builts your usually limited on upgrades, which I don't know if that is an issue or not. The one benefit that you have with a pre-built is that "you" don't have to support the computer! Dell/HP/Gateway/eMachines do, so that can be a blessing in disguise.