You're right, I figured that out now :confused:
No need to enter a key, just re-activate. Maybe use slmgr /ato if needed.

If you would like to avoid a complete re-install and you have a spare harddisk lying around then you can
follow this procedure to create the hash code needed on Microsoft's servers.
Then the next...

I have a tip for you then: if you have a spare harddisk lying around I would:
- create a Windows 10 installation USB stick or burn it to DVD
- disconnect all your harddisk in the PC
- only connect...