Providing your LW connection really is ok (all green/blue bars), try the fixes below.

1. In LW go tools > options > searching > basic & check whether the 'show license warning' box is ticked. If it does, untick it > Apply > ok...see if that makes any difference.

2. Problems with the search

3. 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 LW's options, you'll have to go back through afterwards & reset things to the way you like them.
Vista users: LimeWire Pref Folder in Vista