Hi,
Please first make sure whether you've inserted the correct product key. For how to find your Product Key for Office 2010, please refer to this article: https://support.office.com/en-ca/article/Find-your-Product-Key-for-Office-2010-1e8ef39c-2bd4-4581-a0ae-5cf25ebed489
Also, have you ever made changes to your hardware? If your hardware is substantially different, then it will be considered as a new computer. If this is the case, you might need to activate your Office 2010 via telephone.
If issue persists, I would suggest you contact Microsoft Custom Service directly for further assistance: http://support.microsoft.com/en-us/gp/customer-service-phone-numbers
Hope this helps.
Regards,
Ethan Hua
TechNet Community Support