okay, see with windows 10 things get bothersome. after you upgraded your windows 8 product key effectively vanished, and windows 10 simple uses the hardware IDs in your system to know it is in the right place.
in order to re install it, you would need to download the windows 10 installer ISO onto a a blank 4.7GB DVD disc, or at least 4GB USB (eight to play it safe) and then use it to clean install windows 10.
the fun part comes with calling microsoft and tell them that you moved hardware and thus need it reactivated...
so do the backup see if it works, and if not be prepared to have to go phone up microsoft.... avoid calling near the afternoon if you are in the US, as it seems the workers if you get a US based one, are more eager to just transfer you into oblivion so as to get out of work early.