Reinstall Java. Use the JRE offline installer here & remove your old version of Java before you install the new one.
http://java.sun.com/javase/downloads/index.jsp

Delete LW's preferences folder. See point 3 here (also point 2 if you've used much older versions of LW in the past).
Fixes for LimeWire

Now reinstall LW & make sure to use the offline installer (not the recommended one). No need to uninstall your original LW, it'll do that automatically when the new version's installed
http://www.limewire.com/english/content/download.shtml

If that doesn't help, try changing compatibility. That's point 5 in the fixes thread.

Also, make sure that LW's on the list of exceptions/allowed list of any antispyware programs, if you're using any.