Hi,
Is it a problem after logging in to the 2 computers, or is it a problem when the login interface does not appear?
Which version of Office did you purchase?
How did you log in to your account? Did you use the Microsoft account to login?
Are both computers on the same network?
Please try to log in to another account to rule out whether it is an account issue.
Please refer to this document to find the appropriate activation method for the user's Office product and try it.
https://support.microsoft.com/en-us/office/activate-office-5bd38f38-db92-448b-a982-ad170b1e187e
Please be a bit more precise to explain your problem so that I can get more accurate solutions to this problem. I’m glad to help and follow up your reply.
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