Try this first: 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. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.

If you still can't connect, give us your details.
System details - help us to help you (click here)

Some of the files you're trying to download are probably fakes. These will sit connecting for ages & then get stuck needing sources forever. Try using the All Types search. Search for artist or album, rather than song title. Go for a file with 10 sources or less, or those with a modem source. There's more info in the 2 threads below
Fake files showing up in search results

How to find music