After a bunch of waiting and a good long chat with tech support, we're up and running at home.
See, they have this service over here called Xtra broadband (as in Extra). Part of your password is xtra, not extra. No worries, but if you put in the wrong password (like, oh, I don't know... extra), then you not only don't get on, you get locked out.
After a while tweaking with things and pulling my hair out, I got a call back (yup, they called me) explaining this and how to get unlocked.