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, so that you can reset things later.
What version of Java are you using? Some people have had connection problems with the latest Java updates. You can either try updating to the newest version here (I have this one & LW's working fine):
Java SE Downloads
or try this older version, which has worked well for lots of people:
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11 Whichever Java version you use, download the JRE offline installer & remove any other Java versions before installing another one.
If you update to the latest Java & still have a connection problem, try the older version
If none of that helps, please give us your details.
System details - help us to help you -> Provide these details when you post!!!