It seems that this ended up not having anything to do with Limewire itself. The issue I was experiencing was caused by a bad uninstall of the Comodo Firewall. It seems that Comodo is well aware of the issue with their uninstaller not functioning properly.

Basically what was happening was that Comodo was still the main firewall, but I wasn't aware of it because I thought Comodo was uninstalled and that I was using the Windows firewall. Everything was fine when I was using the previous version of Limewire because Comodo had been told to allow that version. When I upgraded to the newest version of Limewire I was not asked to allow it by Comodo thus unable to connect.

To Fix the Comodo issue:

Download Comodo Uninstall.zip
(You may have to register on the Comodo forum to access the file otherwise it might not show up.)

Extract both clicapi.dll and fwconfig.exe to your hard drive on the same directory that you had Comodo installed on. Most commonly C:\

Go to START, RUN and type c:\fwconfig.exe -uninstalln and hit ENTER.

To Fix Windows displaying wrong information in Security Center:

Go to START, RUN and type cmd.exe and hit ENTER.

At the Command Prompt type NET STOP WINMGMT /Y and press Enter. Then type exit and hit Enter again.

Go to C:\windows\system32\wbem and delete the folder Repository.

Reboot windows. The folder will be recreated by the Security Center and will display the correct information.