In the last couple of days I have been connected to LimeWire but have gotten zero results from any search. Everything else is working fine, even the search process goes through its normal steps, but there is never anything displayed when the search is completed.

If LW's connected properly, 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

Thanks for the advice. I've tried the first two remedies you've suggested but have had no luck.
I'm preparing to try the third but since it requires LimeWire to be closed it may take me a while to get a result because connecting to it sometimes takes a long time.

I was able to reconnect to LimeWire without delay this time but unfortunately there was no improvement in the problem. What is alarming to me is that everything else is working fine...

After you deleted LW's preferences folder, did you have to go through the setup wizard again?

Had you changed LW versions just before the search results problem started? Which version of LW are you using?