I'm no expert, but I have successfully restarted killed downloads. If your search results are gone, you need to start a new search for the file you killed. If you forgot its name or spelling you should be able to find the file name in "My Documents\Incomplete". In the search results, the file you were downloading will have a different icon (white doc icon with a slash through it) in the Quality column. If you download the the same file, it will pick up where it left off. If you wait more that 7 days, the partially downloaded file in the Incomplete folder will be deleted and you will not be able to restart it where you left off.