2 things; 1. if you're using windows XP then disable your XP firewall: go to the control panel, double click on Windoze Firewall, check the disable box. And then configure your other firewall according to directions here: 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)
2. Check the version of Java you have. If you have version 1.5 then perhaps that doesn't run well on your particular system. Going back to 1.4.2 might do the trick. Uninstall Java using Add/Remove control panel. If you have 1.4.2 then try 1.5 instead. Follow the instructions given here for a healthily installed Java:
Fixes for Limewire & if still problems, try the other options in the link.