Sounds strange. If you are absolutely sure that nothing is blocking Limewire on your end, then try scanning your computer for malware, and after that do a clean install of both java and limewire. Use the offline installers for both.

When uninstalling Limewire use the Start>Programs>Limewire>uninstall and then do a search for Limewire afterwards and delete everything except your downloads. If you keep your downloads in the default shared folder then move it somewhere so it isn't registered by Limewire on the new install. Delete the incomplete folder as well.

Then after removing Java as well, reboot your computer and scan your registry for entries left behind by either program and delete them. Reboot after doing this. (note: remember to make a back up just in case you delete some entry you shouldn't have)

If you do not have a registry cleaner then try this one: (By the way this little program is quite good for many other things as well)

http://www.ccleaner.com/

Now download Java and Limewire. For Java try this one Java Runtime Environment (JRE) 5.0 Update 9 (Remember offline installers for both)

http://java.sun.com/javase/downloads/index.jsp

www.limewire.com

Install Java first and then reboot before installing Limewire

If this still does not work then I would seriously start thinking about calling your ISP's help desk again.

BTW I would not keep running Limewire unprotected. When you get it back up and running start adding all your security. Firewall, antivirus and router back into the mix.