(USAFRet) interesting question, as there is no license key any more as such, what will make them think that this is a changed build, they only have indications it is a new build.
(cja711) So to force them to recognise your new build as an update and give you the option to ask them to move it (which they can refuse), install win 8.1 using your original key, at this point they'll accept or reject the license. If accepted update to win10, and then reinstall win 10 so that you are clean.
If they reject the upgrade then buy win10 and install from scratch.
Originally your machine ha cost built in for a massively discounted win 8.1 license, discounted because it was tied to one machine, so you are being conned into buying a new license...