You might not have a modem or router then... does your computer plug straight into the wall with no devices between the computer & the connection?

You might have to go see your school's/building's admin & ask them to help you out. Before you lost your lease, had you made arrangements with them to use p2p? Just a guess, but it sounds like they've stopped letting you use p2p.
Can other people in the buliding use p2p apps?

If you have no router & you're sure that ZA is set up properly, it's worth finding out whether the computer admin has changed anything.
Do this port test, see if it works
http://www3.limewire.com:6346

If that test doesn't work, something is blocking LW's default port. Do you remember which port LW used to connect through?
It's possible that changing to a higher port number would help but it's probably worth getting info from the school/accomodation first