Try updating your Java to this version. Use the JRE offline installer & remove your current Java version(s) before installing this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

If that doesn't help, If that doesn't help, delete LW's preferences folder when LW's properly closed. See point 2 here & also point 3 if you've used newer 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.

Your ISP (internet service provider) is the company that you pay for your internet

If you want help with the firewall issue, we'll need the brand & model of your modem/router. If you don't see anything on the unit, have a look underneath.