If you reinstall Windows, Office will need to be reinstalled also. For that, you'll need the Office Product Key.

Question: how do you know Windows is not already using the Windows product key on the laptop case?

FWIW, unless you're installing a different Windows version/edition, it shouldn't make any difference which Windows product key you use (unless you try to use a non-genuine one).

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Cheers,
Paul Edstein
[Fmr MS MVP - Word]