Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Hello B B,
I understand why you want the product key, especially when Office 2016 worked before and the key no longer appears where you expected it in the Store. You should not need to buy Microsoft 365 just to check a copy of Office Home & Business 2016 that you already purchased.
If the key was redeemed previously, Microsoft says Office 2016 can be activated by signing in with the Microsoft account used to buy or set it up, rather than entering the key again. Could you check whether Office Home & Business 2016 appears under Services & subscriptions for that account?
I also wouldn’t rule out seeing a key online in every case: Microsoft documents a View product key option for certain one-time-purchase Office installations, though I can’t tell whether it applies to your purchase. If Office 2016 is listed but still won’t activate, please share the exact wording of the activation prompt, without posting a product key or account details. That will help distinguish a sign-in problem from a different activation issue.