Well it sounds as though you have absolute no control over your net hardware. The best I can suggest is to force ip:
Force IP instructions & sample image
Or try another version:
http://www9.limewire.com:82/download/ OR
http://www.oldversion.com/program.php?n=limewire or even the beta:
http://www.limewire.com/english/content/beta.shtml
You wouldn't believe how much a difference a single version can make but it can! There's not dramatic differences b/w the versions of LW 4 but certainly some improvements & corrections.
But it does surprise me you aren't protected by a firewall & anti-virus/spam/spyware/adaware