If your laptop is turned off it cannot do anything. It needs to be on to work.
You may be able to turn the screen and close the lid, with the laptop still running so it can continue downloading. To do this you will need to modify your power options in the Control panel.
I downloading a full episodes drama with a bittorrent software. Can I turn off my laptop while it still active download? I'm afraid I need to download it back if I turn off my laptop.
Turning your laptop off won't delete/cancel the download, it will just stop until you turn your laptop (and bittorrent) back on, after which it will simply resume from where it left off before being shut off.
