LimeWire will not download the TV episode that I wanted to watch. It was making 0% progress. It had 6 hosts. How can I get it to download?

Manually search for more sources. Even delete it from your downld list & reselect it from the search results. This can sometimes invigour it to downld properly. Make sure you're not too busy downlding other things. Also wait until LW settles down. Too many people expect LW to be active as soon as you open it. But the fact is depending on how many incomplete files & shared files you have, LW may take b/w 5 to 25 or so mins to settle down. So don't rush things!