Did you use the offline installer of LW 4.12.4 ?
http://www.limewire.com/
The same is necessary for Java (using the JRE offline installer for your OS):
http://java.sun.com/j2se/1.5.0/download.jsp
You should remove LW using the uninstall.exe (START>Programs> Limewire>Uninstall).
I suggest you remove both, LW and Java, reboot your computer, install Java, reboot again and then install LW.