Once upgraded to Windows 10 future Windows 10 installations will accept just the motherboard serial being the same. It's also possible CPU and HDD serials would be used.
However when reinstalling Windows 7 the same rules apply that did before. You'll need a key unless its SLP. Windows 7 in my experience is more touchy when changing the storage device however this is still legal for you to do so if it fails you should be able to call to activate.