Sure you can build a PC for around $200, it won't be the fastest thing around but if you just want it for surfing the web and some mundane word processing, here you go:
Pentium Dual Core ~$67
http://www.newegg.com/Product/Produc...82E16819116076
Any micro ATX LGA 775 mobo should have good enough IGP ~$40:
http://www.newegg.com/Product/Produc...e=&srchInDesc=
RAM, one will be slow, two would be nice if board has dual channel small little boost ~$15-30:
http://www.newegg.com/Product/Produc...e=&srchInDesc=
Case, can find decent ones closer to $50, but that would be pushing your budget, so ~$25 [note: PSU included while 400w pretend it is a 250w haha]:
http://www.newegg.com/Product/Produc...82E16811164138
DVD+keyboard+Mouse+HDD: ~$70-80
Buy a cheap hard drive, even at 160GBs should come in under $40
http://www.newegg.com/Product/Produc...e=&srchInDesc=
Buy a cheap Mouse+Keyboard combo for like $10:
http://www.newegg.com/Product/Produc...82E16823157010
DVD writer/burner are now under $30, get a non burner $20 easy:
Mix and match, monitor will be another issue, but you can use your TV with the right IGP for that, especially if you have a new fangle HDTV. Also no operating system, that tends to be the biggest expense when building cheap.
I've built lots of cheap PCs for the sole purpose of surfing the net and word processing. Again, this won't be a very fast computer - but enough.
Sometimes at these prices, it just might be safer to go OEM since they include software bundles and sometimes a printer haha.