Boot via Windows installation media (DVD, USB flash drive, etc)
When the "Windows Setup" window appears, press Shift + F10 to open a command prompt
Launch one of these tools from the command prompt to retrieve product key from BIOS / UEFI:
Windows OEM Product Key Tool 1.1 - Purpose-built app; simply returns the product key
FirmwareTablesView - Displays list of firmware tables; look for "MSDM" under Signature column or "Microsoft Software Licensing Table" under Description column
RWEverything - Digs deep for a plethora of hardware details; head to ACPI > MSDM > Data.
To identify which version of Windows the recovered product key corresponds to:
Ultimate PID Checker - Works with product keys from XP through 8 (not 8.1); runs inside the Windows installation environment.
ShowKeyPlus - Works with product keys from Windows 7 through 10; does not run inside the Windows installation environment. (UPDATE: Users have flagged GPL violations (to which the author nesciently replied, "GPL does not mean open source - it's freeware only."), missing source code, and cloaked network activity.)
For OEM computers still shipping with Windows 7 or 8.1 (slated to end on October 31, 2016), the firmware-embedded product key likely differs from the product key on the hard drive. Recover the latter with ProduKey.
For more information on embedded product keys, see Windows 10 Embedded Product Key Tool and Where is my Windows product key, and how can I tell that my Windows installation is genuine?
/windows | Sep 04, 2016