Try these things:
1. Install Java 1.5 from here using the "Offline" installer:
Java 1.5 (take the JRE)
2. Configure your firewall so it allows LW full access (advisable not to have 2 active firewalls b/c they can interfere with each other);
Firewall configuration instructions (click on link)
3. Delete your LW preferences folder. You'll find it either with step 2 or 3:
Fixes for Limewire
4. Install LW "Offline" version from here:
http://www.limewire.com/english/content/download.shtml