Appears that both Java and LW are a little outdated. If you want to update Java, See below.

Try uninstalling all versions of Java from add/remove programs and then use Crap Cleaner to clean the registry.

Try updating to the latest version of Java here Java SE Downloads (First JRE 1.6.10)Useing the JRE Offline Installer.

If the latest update gives you any problems, try this older version, which has worked well for lots of people: Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11
Hope this Helps.

If you want to update LW see www.limewire.com.

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I take it that you believe that this is a Java problem. I just want it in plane English so that when someone does a search it will come up in the search results.