Try removing your current Java & then reinstall JRE using the offline installer here
http://java.sun.com/javase/downloads/index.jsp

Then reinstall LW using it's offline installer
http://www.limewire.com/english/content/download.shtml

You could also try deleting the limewire preferences folder(while LW is closed) point 2 & 3. Fixes for Limewire when LW isn't operating as it should!

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If it ain't broke, fix it till it is!