Did you use the offline installer for Java? Try again. Download using the JRE offline installer (point 1 below)
Fixes for LimeWire
Go to add/remove programs & remove your old version of Java before installing the new one.

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

If that's no good, try changing compatibility (point 5 in the Fixes sticky) or deleting the preferences folder (points 2 & 3).

Also make sure that LW's on the list of exceptions/allowed apps for any antispyware programs you're using.