Have you tried Java 1.6? Use the JRE offline installer & remove any old Java versions before installing the new one.
http://java.sun.com/javase/downloads/index.jsp

Delete LW's preferences folder when LW's properly closed (check in task manager). See points 2 & 3 below. If you've used LW versions older than 4.9.34, you might have a folder in both locations. If you've only used later versions, just look in point 3's location.
Fixes for LimeWire

Also try changing compatibility (point 5 above).

Otherwise, check to see that LW's on the list of exceptions/allowed apps for any antispyware & security programs you're using. Some people have had trouble with their antispyware seeing LW as a threat & preventing it from opening/running.