Andrewcw's timeline is wrong, mandatory UEFI and OEM keys in the firmware started with Windows 8. I have an early 2013 laptop that can prove that. However, Billiam29, you are right.

You can use any OEM CD with the Key that is physically on the computer, it might require a call to activation services but it will work fine. And no, original OEM isn't encoded into the product ID.

SEE: Windows 10 turns five: Don't get too comfortable, the rules will change again "Installing this Intel generic graphics driver will overwrite your computer manufacturer (OEM) customized driver.