A few things i can think of:

1. Re-search the item, and use the right-click search tab option of Get More Results. If you see the download icon but your download has not started, then cancel your download, re-select from search results. I do this often. It worked with LW 6 years ago, still works now.

2. Tip: Purge the Downloads Queue! (click on blue link). This will get rid of any fake files you may have accidentally selected also and put less pressure on the LW program.

If still problems then:
3. Make a note of all your option settings, CLOSE LW, then delete your LW preferences folder: instructions here: Point #2 & 3 in Fixes for Limewire (sample image included at bottom of page.)

BTW have a look at the topics here MAJOR TOPICS for Upload/Download HELP. Those about fake or corrupt files, especially audio ones. This will give you an idea of what sizes to stay away from.