Well, that's a shame, let me see if I can help you:
1 - If your broadband does not need a login and password -- you just connect your MBA to the Ethernet adapter and after a few seconds you are online -- you don't need to do anything on your broadband modem. All you can do to make sure is turn the broadband modem off and on, just in case.
2 - Even if the connection between the Airport and the broadband modem don't work, your MBA should connect to it fine.
3 - On your MBA, go to System Preferences and click on the Network Icon. Be sure that on top of it, on Location, it is setup to Automatic, and the on the left column your AirPort is On, with a green led.
4 - Once your MBA's AirPort is on, at this very same screen, you should select you AirPort Express connection -- I can't remember what's its name right out of the box, I think it might be "AirPort Express" or "Default". Select it to connect.
5 - After that, fire up the AirPort Utility. It should connect and then you can start the configuration of your Wireless network.