You would have to revert back to your original operating system version first (Windows 7 / 8x), then run the official upgrade to 10. Run that for a few days in order to assure that Microsoft indexed your hardware fingerprint. After that, you can wipe the drive and perform a clean installation of Windows 10.
During installation and first startup, whenever you get asked for a product key, simply skip it. It isn't needed and your Windows installation will get activated automatically the first time your laptop goes online.
Alternatively, you now should be able to use your official Windows 7 / 8x product key for activation. However, I find the above method much cooler! Never ever having to deal with product keys on the device again is just amazing, especially if you have to install Windows relatively often on the same machine.