Files that sit connecting for ages & then need more sources forever are usually fake files.
Fake files showing up in search results
How to find music (tips for video, too)

Is it really happening with every song? Do a test...try to download an old song (2 years plus) with 10 sources or less. If this really is happening with every file that you try to download, try this: Delete LW's preferences folder when LW's properly closed. See point 3 below (also point 2 if you've used much older versions of LW in the past...there could be a folder in either location).
Fixes for LimeWire
Deleting that folder will kill all of your settings within options. You'll have to go back through afterwards & reset things.

As for your connection only getting to 'fair'...we can't guess your setup
System details - help us to help you