Hi EricFAust,
From your post, I’d like to confirm whether you have installed the latest software from Office 365. If not, I understand that you can’t open any office document since you have uninstalled all of the office 2010 application. You can install the latest Office (Office 2013)instead of the older Office 2010 Pro.
To install Office, Here are some steps:
1. Sign in to Office 365 Admin Dashboard .
2. Click the settings menu on the right of navigation bar> Office 365 settings.
3. Go to Software page> Office
4. Select the language and version, then install.
If there is anything unclear, please feel free to let us know.
Thanks,
Mills Fan