Does this happen with every file that you try to download? I mean every single one Do a test...try to download a song that's 2 or 3 years old & choose one with only 1 or 2 sources, or a single modem source.

There are fake files on the network that sit connecting for ages & then get stuck needing sources forever. These things won't ever download.
Fake files showing up in search results
How to find music

If it's really happening with every file, try deleting LW's preferences folder when LW's properly closed. See point 3 below. This will kill all of your settings within options, you'll have to go back through afterwards & reset things to the way you like them
Fixes for LimeWire