Hello Leon,
How we get out of pickles is usually a function of how we got into them. I see you're on Win10 now, from Win8.1, last thread of Your's I'm aware of.
I few variables known may enlighten the way to a solution:
1. Was this a straight upgrade to Win10, run from within Win8.1?
or
2. Was a new drive installed, and Win10 simply installed cleanly?
If #2, was the Windows key/serial entered during the clean Win10 install?
If not, a) this will need to be entered, and b) the correct version (Home or Pro) must have been chosen during install. A wrong choice at (b) will need a reinstall with the correct version.
The point made earlier about activation over the phone is a good one. You can force that along by denying the PC any form of internet connection, then restarting. Phone options will be more available then. If it's an automated call, you're good. If it's a chat with a friendly Indian, be sure to state that this is the SAME PC, with a reinstall. They may ask your contact details. Refuse kindly, and ask "Can you please run the phone activation process for me, that is all".
For the record, my fave way is to do the upgrade within Windows, which notes the activation with Microsoft (The digital licence). After that, do a wipe and clean install. You can then trash windows anytime, and it will re-activate once it has internet access automatically.
Tell us how you go