Hi,
Does the activation key issue happen to all computers? What's the updates have you installed, for Windows or for Office? What's your detailed Office 2013 version, Click-to-Run or MSI version? Activated by Product Key or a Microsoft Account?
Please go to Control Panel > Programs and Features, select Microsoft Office 2013, click Change > Repair (or Online Repair for Click-to-Run version) to have a try.
Regards,
Winnie Liang
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