T> It keeps
T> asking me for the passwords to two available wireless networks. One is
T> the correct one. One is the incorrect one.

Once you've successfully connected to the correct one then it should
log into that and not bother with anything else. So, have you put in
the key for the correct wireless network and got connected to it ?

If you aren't using wireless then you can turn off the wireless side
of things. Right Click on the network icon on top right and click on
the 'Enable Wireless' bit to clear the check mark.