The number in the green circle shows how many files you're sharing

Rather than turning off your software firewall, it's better to configure it to allow LW.
User Cant Connect - LimeWire

Normally, when files sit connecting for ages & then get stuck needing sources forever it means you're seeing fake files. Check out these 2 threads for more info & tips.
Fake files showing up in search results
How to find music

But...if you're seeing this with every single file that you try to download (do a test, look for an old song & try to download a file that has 10 sources or less) try this: Delete LW's preferences folder when LW's properly closed. See point 3 here & also point 2 if you've used older versions of LW in the past (there could be a folder in either location).
Fixes for LimeWire
This will kill all of your settings within options, you'll have to go back through afterwards & reset things. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.

You could also update your Java to this version. Use the JRE offline installer & remove your current Java version before you install this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

You could also try port forwarding for your router, using the instructions here.
Port Forwarding for the Dlink DI-704
Don't forget the step of setting up a static IP address first. LW's listening port, port in the 'manual port forward' box & port forwarded within the router all have to be the same number