What happens when you try to download? Does the file you've clicked on move down into the download pane? If it doesn't, just check that it's not a license problem (click on link)
License

If the files you're trying to download are stuck 'connecting' forever, you might be trying to download fakes. In this case, search again. Vary your search terms & try the All Types search. Stay away from files with huge numbers of sources, instead go for a file with 10 sources or less.

Double check that your maximum downloads aren't set at zero (tools > options > downloads). If all else fails, delete the LW preferences folder...points 2 & 3 below. LW must be closed first.
Fixes for LimeWire