When you're connecting to a home or office network using your AirPort card, your computer is not "connecting to the Internet." It's connecting to a LAN. You apparently have your computer configured to connect directly to your DSL modem, which is why you get PPPoE messages-PPPoE is the protocol most DSL providers use for connection management.
I'd delete that network location and set up a new one that you configure to join a LAN. Once you delete the existing location, your computer should detect the Extreme base and tell you there's a wireless network available. That should start the setup process for you-follow the prompts and refer to the Apple Help for Networking if you don't understand something. If it still doesn't make sense, check back here.