You can also try just powering off the cable modem, connecting the one computer to the other, and powering the modem back up after a minute or two... it's an annoying workaround, but it does work. Nerdinium is right about the MAC address thing. I used to have Comcast, and their modem did the same thing. It's a pain in the neck.

If you're going to be sharing your Internet connection on a regular basis, you should probably get a router to get around the problem.