I use Auto Power On & Shutdown for this purpose. Get it from
www.lifsoft.com
It is an excellent utility for same purpose. It can start PC from hibernate condition at preset time and can also run specified program.
I use Flashget to download from rapidshare.com (I have premium a/c). I also use uTorrent for downloading via torrent. I have set my preferences to start downloading on starting up the program (for both Flashget & uTorrent).
I put links in flashget and add torrent to uTorrent and at about 11 p.m. I hibernate my PC. I have set Auto Power On & Shutdown to start PC at 2.30 a.m., to have safe margin. Do not set exactly 2 a.m. as it may inflate your bills, if counted. Auto Power On & Shutdown starts flashget at 2.35, uTorrent at 2.40 and Rapidup (for uploading to rapidshare) at 2.45 am. I manually stop all programs at 7 a.m. But you can also set to terminate programs in Auto Power On & Shutdown.
Note that Auto Power On & Shutdown can start PC from Hibernate condition only and not if it is completely shut down.
Hope this serves your purpose. I get very good results from it. I usually download 70-80 GB per month using this trick.