I have run into this (if I'm understanding your situation correctly). I had a Windows 8.1 machine and upgraded it to Windows 10. I THEN built an entirely new machine from the bottom up. New motherboard, RAM, EVERYTHING. I took out my harddrive from my old machine which had Windows 10 in it thinking this is going to be great. I'll be set. I ended up booting up my new machine and Windows 10 saw everything was new and saw it as a different machine entirely so it asked to re-authenticate. I tried to put in my old Windows 8.1 key however this didn't work. I called Microsoft support and explained the situation. They informed me that I needed to basically start from scratch and have the new system have Windows 8.1 on it, THEN authenticate it and THEN upgrade to Windows 10. In short, if I'm understanding your problem as I read it, you need to start with the original disks with the new machine, authenticated and THEN upgrade to Windows 10.
Dale