Okay, something weird is going on.
My home Internet setup is like this: The cable modem my ISP gave me is connected to a router. The router has cables running to my computer and my roommate's.
If I try to run a cable directly from my computer to the cable modem, I get a "connected to the Internet, but no Internet access" error. On the other hand, if I unplug the cable modem from the router, I can still connect just fine.
What's going on here?