Was windows 10 on the PC already? If so, was you old user linked to an email address?
If Win 10 has already been on the PC, its not stored in the BIOS, its actually stored on the Microsoft servers now. When you to install win 10 and reach screen where it asks for a licence, click "I don't have a key" and win 10 will continue to install and check the servers once installation is complete, and reactivate PC if licence is still tied to the hardware
If it remains inactivated, have a look at this page as it shows how to access the Win 10 activation troubeshooter -
https://support.microsoft.com/en-us/help/20530/windows-10-reactivating-after-hardware-change
You can get the win 10 installer from here - download the
Windows 10 media creation tool and use it to make a win 10 installer on USB
but if you didn't have win 10 already, you would still need to buy a license key.