You need a router, either wireless (which I am a fan of) or cabled. The reason is that in order to access the internet, you need to have a valid IP address assigned to both machines, but you can only do one at a time unless you have two separate broadband cables run into your house (rather extravagant to say the least

).
SO you get yourself a router, and the router automatically assigns a different IP addy for both of your machines, and you set your computers up as a network. Now you can run them both online at the same time, totally independent of each other. D Link makes a really great router for a low price; you will need one router and two NICs (Network Interface Card). If you want to go cabled, you can use the NIC that is already on the back of your computer; if you want to go wireless, you must buy & install a wireless NIC in each computer and get a wireless router.
Hope this helps.