There are loads of fake files around now, which typically have heaps of sources & are often new releases. They'll sit connecting forever but never download. Stay away from files with huge numbers of sources, go for a file with 10 sources or less!

If you find the connecting issue happens with all files, try deleting your preferences folder when LW's closed. See points 2 & 3 here
Fixes for LimeWire
This will kill your settings within Options, you'll have to go back through & reset things afterwards