Which firewall are you using?
In LW, click on help > about LW & it'll show which version of LW you have.
Have a look at your router & see if you can find a model number, if nothing's showing on top, have a look underneath.
What security programs are you using?
Are you using the router with UPnP (if the router supports it) enabled or port forwarding set up? Or neither?

Some people have had connection problems with the latest Java updates, try this version instead. Download the JRE offline installer & remove any other Java versions before you install this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

Also 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 change 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 first, so that you can reset things later.