Try these steps:
1. Open your Add/Remove Programs control panel & remove all versions of Java listed.
2. Install Java 1.6 beta from here
http://java.sun.com/javase/6/ (choose the JRE) "Offline" installer which is 15.72 MB
3. Delete your LimeWire preferences folder, see steps 2 & 3 here
Fixes for Limewire (sample image at bottom of page.)
4. Then try opening LW.
BTW if you have a spyware program that thinks LW has spyware (it doesn't!) then put LW on the safe list. Spyware programs like PestPatrol do damage to LW, meaning LW needs to be reinstalled.