If it's connecting for more than one minute then chances are it's a fake (but will be at zero % downloaded.)

If files go into Queued mode, you can use the resume button to help, LW has in recent months introduced a bug where queued files do not continue when they could. O.o

If you have a large number of incomplete files, then it is wise to do this: Tip: Purge the Downloads Queue! (click on blue link). You will notice a fresh difference after you do.