Bingo! I found the solution to my LimeWire bad connectivity problem which was stopping any items being downloaded.

1. Close LimeWire and also remove any LimeWire icons that may be sitting in your Taskbar.

2. Go to your Program Files and delete the entire folder that's named LimeWire. Don't open it up - just delete the whole thing.

3. Click open your LimeWire shortcut icon that's on your desktop.

That's it. Worked for me.