If you want cheaper PC's it might be better to get them laptops or netbooks. They come with a wireless card and can double as portable entertainment to keep them happy during long car trips. Netbooks (mini laptops) are good for web browsing/Facebook/e-mail/instant messaging/etc. and basic (non-3D) games and when equipped with hard drives can hold a good amount of music too. I got my netbook for $250 after upgrades (added Bluetooth, Windows 7 Pro to a $200 netbook) and love it for on the go and basic computing. A netbook + monitor/keyboard/mouse can be had for less than $500 (USD) and works double duty as both a basic desktop setup and a portable computer. Netbooks are about the size of portable DVD players (and you can rip DVD's using a different PC with a DVD drive to them) so they work well on the road.
I bring up travel because when I was 11 (and still to this day) I need to be entertained during long car rides (we go on a 11 hour ride and back several times a year to visit family) and once I got my first laptop I couldn't go back.
A netbook+monitor allows them to do homework (netbooks run Office pretty well if they're running Windows), browse the Internet, chat with friends, and even video chat (most netbooks have webcams) while being cheap. The kids won't need dual core or quad core CPU's or 4GB of RAM anyways.