If the HDD's OS has already been upgraded (via the free upgrade) to Win 10, you will have to get a new product key (license) when you move it to new hardware (the motherboard is key here). Also, one license = one PC. You can't move to a second system and get 2 systems for the cost of 1, so to speak.
When MS put the free upgrade of 10 out, it becomes tied to the motherboard (like other OEM installs). I went through this very issue with MS after having to replace a defective motherboard in my father-in-laws PC in November. It was a pain to get MS to give me a new product key. They may, or may not, do for you.
Good luck.