I guess your appartment managers blocking the gnutella host caches, LimeWire tries to connect to. - Other p2p-applications aren't as easily blocked as LimeWire.

A workaround can be, to get a gnutella.net file for LimeWire (copy it into your LimeWire directory).

You can download my latest gnutella.net with addresses of gnutella ultrapeers here:

ftp://whitedragon.dyndns.org/gnutella.net