I have also tried using another router that I have on hand: a linksys BEFSR41. This router produces the same results as our main linksys BEFW11S4 router, so I don't believe it is a router issue.

I think my next step is to try installing a fresh install of XP, to see if this produces anything different than the Vista OS.

I tried calling the tech support offered with the computer, and they said that since I could get a connection when the machine is directly connected to the modem that as far as they are concerned the machine is working properly.