18greens,
There is no such thing as a Wireless Built in Modem, that would be an Internal Modem, but it is not wireless.
You would need a Wireless NIC in order to connect to your BT Wireless Router.
You might need to check with BT, there is a good chance they limit the number of users that can log on at one time.
With a standard Wireless Router, you can log into the Router and create a Key. Then you copy the Key and put it in the device you want to have log in.
Take Care,
Richard
P.S. That is just general info, since I have not seen a Voyager 2000, so I cannot be more specific.