I agree to purchase a router yes. However, I do not recommend linksys WRT54G This is the same exact model (depending on firmware) I was having problems with it the doctors office. Took it home hooked up in 2 minutes.Buy a router. I recommend the Linksys WRT54G. (<$60)
Go to the configuration screen... Tell the router to use your PC's MAC address.
Use both computers at once.