In order to fix the connection issue, go to Start > Control Panel > System and Security > Windows Firewall > Allow a program through Windows Firewall and check the box next to LimeWire. If you can't find the software in the Allowed programs and features window, press the Allow another program button, navigate to the installation directory, select the executable file and press Add.
After that, from the Advanced Settings select Inbound Rules > New Rule. Check the Port box, click Next, select All local Ports and follow the self-explained steps. Also, make sure that your security program doesn't block the connection.
If the problem is not solved, try uninstalling the application and then installing it again. If you still have issues, I suggest you use a similar program from Software Informer database.