Did they tell you to make sure to use the Java offline installer?
http://java.sun.com/javase/downloads/index.jsp
Make sure to remove your old Java version before installing the new one.
You could try deleting LW's preferences folder, see points 2 & 3 below
Fixes for LimeWire
You could also try changing compatibility to Win 2000 or NT, that's point 5 above.
If you need to reinstall LW, make sure to use the offline installer, not the recommended (online) one
Have you added or updated any antispyware or security programs recently? Just make sure that LW's on the list of exceptions/allowed apps if this is the case.