Seems to me this is one of the areas LW lets users down with torrents.
With some other 'torrent only' programs such as uTorrent & Vuse, it is easy as pie to restart torrents if something goes wrong with the computer that mucks up the downloading. Question is what the exact problem is. You could arguably try using either of those programs mentioned & open the torrent up with them to see if they recognise the previous download % & continue the torrent. LW 5 unfortunately does not have resume functions, once a download vanishes from the download window for whatever reason you cannot restart it usually. For gnutella network files you can go back to LW 4, resume the incomplete downloads then revert back to LW 5, but I do not know if this would work with torrents.

Are the incomplete torrent files showing up in the Download window at all? If yes, I wonder if someone 'kick & banned' you for downloading using LW.