Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Hello Callahan,
I would suggest you to run the fixit available in the link below which would remove the Office traces automatically from the Computer.
http://support.microsoft.com/kb/2739501
Once done, try to re-install Office 365 and verify the status.
If the issue still persists then you may follow the general troubleshooting steps provided in the article below for installation failures of Office 365 and check if that helps to resolve the issue:
http://support.microsoft.com/kb/2822317
For further queries, reply and we would be happy to assist.
Thank you.