Hi Ironcladdread,
Would you please let me know which Office 365 service you are using, Office 365 for business or Office 365 for home?
Based on my experience, for Office 365 for business service, generally, after clicking "Sign in to an existing Office 365 subscription", we can activate the Office via entering user account and password.
In this situation, please try accessing the Office 365 portal first and then I hope you don’t mind trying re-entering the user account and password to activate it.
However, for Office 365 for home service like Office 365 for Home Premium, actually, we have a dedicated support regarding it, in order to efficiently investigate the root cause of the activation issue on the Mac, I recommend you post this question with detailed description on the Office 365 Home Premium forum where is staffed by many experts specializing in this kind of problems. You can get this problem resolved more efficiently there.
Office 365 Home Premium forum: http://answers.microsoft.com/en-us/office/forum/office_365hp
Thanks,
Ida Qiu