First update your Java. Use the JRE offline installer here. Remove your old Java version before you install the new one.
http://java.sun.com/javase/downloads/index_jdk5.jsp

Now delete LW's preferences folder (check in task manager to make sure LW's not running). See point 3 below, or if you've used version 4.10 or older check point 2 as well...you could have a folder in the old location.
Fixes for LimeWire

After that, reinstall LW. Use the offline installer (not the recommended one). No need to uninstall the previous version, it'll happen automatically when the new one's installed.
http://www.limewire.com/english/content/download.shtml

See if that fixes it