I just found an instance where the Windows 7 product key was required for activation.
My wife has a Dell Inspiron 1545 notebook computer that had Windows 7 Home Premium. I upgraded it to Windows 10 - 10240 in July 2015 and it activated right away. I just got a good deal on a 120GB SSD drive and installed that in the old notebook, replacing the old spinning hard drive. Tried to do a clean install, skipping entering the key, and when Windows 10 - 10586 booted up it said it was not activated and wouldn't activate automatically.
So, I tried the new option of entering the Windows 7 Home Premium key that came with the notebook computer. In this case the Windows 7 key was printed on a label that is under the removable battery. It worked entering the Windows 7 Home Premium key and Windows 10 - 10586 activated instantly. I used the Settings, Activation, Change Product Key option to enter the Windows 7 Home Premium key.
So if a clean install of Windows 10 - 10586 doesn't activate automatically, try entering your old product key from Windows 7.