Reinstall Java. Use the JRE offline installer & 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 below. If you've used LW versions older than 4.9.34, you could have a folder in point 2's location as well.
Fixes for LimeWire
After deleting that folder, you'll have to go back & reset all of your LW options.

If it's still no good, right click on the LW icon & change compatibility...see if that helps.