I installed Limewire and the blue bar shows progess in the searches but, even for the classic popular songs which should show lots of hits, there are zero results. I've used Limewire before and never encountered this problem. Can anyone help?

Are you connected properly (how many green connection bars do you see)?
If your connection is ok, try this: Problems with the search

And if that's no help, 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 kill all of your settings within options, you'll have to go back through afterwards & reset things.

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.

If there's a connection problem, please give us your details.
System details - help us to help you (click here)

Hello Birdy,

Thanks very much for the quick and detailed response. My connection was fine.
I started from scratch and installed a version from the Limewire website, and the problem has disappeared.

Cheers
Oksana