You could try removing your old Java & reinstall with the offline installer here
http://www.java.com/en/download/manual.jsp

Now reinstall LW using it's offline installer
http://www.limewire.com/english/content/download.shtml

If you're running an antispyware app, make sure that LW is on the list of exceptions/allowed apps. Some antispy things will see LW as a threat (it's not!).