Have you tried an older version of Limewire, to see if that one connects? Some people have trouble using the new version.
If not then uninstall both your Limewire and Java (Remember to also delete the Limewire folder in AppData) and reinstall both (newest Java, older version of Limewire). You can find older versions here:
Download LimeWire Basic 5.0.7 Beta - FileHippo.com