Go to LW's preferences > Advanced > Performance and disable TLS. Then press apply. See if this makes a difference.

TLS always seemed to be a problem for connecting properly on my Mac when using LW4. When disabling this option and restarting LW the firewall icon would usually go away.

LW 4's UPnP was a little less reliable to kick into action than the LW 5 equivalent.

You are obviously using a cable modem or router. This might be the source of the firewalling issue. May we know which brand and model?

I am rather curious to know whether you are able to access the LW preferences from under the LimeWire program menu on the toolbar next to the apple icon far left of screen. The preferences option stopped showing for me in early 2010. I have to use the Library window's configure shares option as a back-door to access the settings.

BTW try search something simple like the word beat.