Ron B mentioned another source of possible confusion.
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EXACTLY what sort of "free offer" came with the computer. The "normal" one has been a "free trial" of Office 365 that lasts only 1 month, after you give them a credit card and email account.
About a year ago another "free offer" showed up. That is a "free" (price built in to computer) 1 year subscription to Office 365 Personal. Unlike free offers in the past, there is no visible product key provided. The key is embedded in a "tile" in the Windows
10 Start Menu. The first time you click on the tile you are prompted for the email account the subscription is to be associated with. If you say "no", the offer is "used up". If you provide the "wrong" type of email, ie a school .EDU account, the activation
fails (probably with no error message) and the offer is "used up".
Since you mentioned "free" Office from school, there is another confusion point. Typically 365 Education requires a .EDU email account to use. 365 Education is based on "business" Office. "Free" office (30 day trial or 1 yr subscription) is based on "consumer"
office that requires a Hotmail or outlook.com email account. If you use the wrong type of email account to try to activate a subscription, the activation will fail.
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"Normally" you would expect to see an error message when there is a failure. But in at least one specific activation situation you won't (I expect there are more). For example. your computer comes with a factory installed 30 day free trial of Office 365.
You don't want to use it, so you ignore it and install a license you already have, such as Office 2010. When you submit your 2010 product key, inside the 2010 application, for activation, somehow Windows passes it to the 365 Free trial. Where it fails, silently.
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My suspicion is that you accidentally "used up" the free subscription activation and are now out of luck.
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I saw a suggestion to try restoring the computer to "factory fresh". It's worth a try, but I'm 99.44% sure that the Office activation tile won't be in that backup image.
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If you have accidentally "used up" the free subscription without successful activation MS and the computer builder will just finger point at each other without resolving your problem. The builder will say Office activation failures are MS's problem. MS will
say they sold the key to the builder, it is their problem ...
Sorry to say, the bottom line is you are most likely TARFU.