Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
So far what seems to be working is an uninstall/reinstall of 2013. Not optimal for sure.
Based on reading between the lines and the symptoms- it appears to me to be primarily Office 2013 clicktorun on Windows 7. No VL/MSI/KMS deployment of 2013 is reporting this issue.
I don't read that it's the Windows updates, but the click2run update barfed.
The past info to uninstall/reinstall:
"To resolve this problem, run the Office uninstall fixit from here: http://support.microsoft.com/kb/2739501.
Next, re-install Office 2013 by logging into www.office.com/myaccount with your registered email address and click Install Office."