Jlamb, Limewire uses Java to run. Need to check what version you have.
Go to Start > Control Panel > Add/Remove. May need to install a different version. See Link below. Seems to work for a lot of people.
Some people have had trouble with the latest Java updates. Try this version instead. Use the JRE offline installer & remove any other Java versions before installing this one (it's easy enough to reinstall a later Java if it turns out that Java's the problem).
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11