Hmmm...Who is your ISP and what security are you running on your comp ??
Here are some fixes that may help (well I hope they do)
Try uninstalling your Java from the add/remove programs and then re-install the JRE offline version....(4th one down)
Java SE Downloads - Previous Release - JDK 5
Then uninstall Limewire using the uninstaller which is found in start > all programs > limewire...then re-install it using the offline installer...
LimeWire: The Official Site for the Fastest File Sharing Program on the Planet
Try deleting your preference folder...
Fixes for Limewire when LW isn't operating as it should
If none of that worked try this...
Right-click the Limewire icon and going to properties and change compatability setting to Windows 2000. (but only if you're using Windows 2000 or later.) Somebody reported changing to Windows NT compatibility fixed their problem despite not using that operating system version.
Right-click on the Limewire icon on the desktop and click on Run as. Then it should come up showing the current user and then switch it over to Administrator. (but 'only' if you're the admin of your comp.!)