Some people have had connection problems with the latest version of Java. Try this version instead. Use the JRE offline installer & remove your current Java version(s) before you install 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 3 here.
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.