After applying the June update to Office 2016 (Preview) 16.0.4201.1002, my OneNote notebooks would not open. The error message was that there were no accounts associated with an active Office 365 subscription. This was a bogus error because all my other Office Applications worked fine, and it only affected OneNote. I deactivated Office from the Portal, and then re-activated it – with no improvement.
The fix was to go into Control Panel and launch an Office Repair (The Online Option, not the Quick Repair).