Hi,
I test on my environment (Windows 10 and Office Professional 2010), I could not sign into OneDrive too and get an error message: Unable to connect to Microsoft OneDrive.

I try to run "OneNote /safeboot" to clear caches and remove all Windows credentials, unfortunately the issue still exists.
Besides, I find a similar thread: OneNote 2010 notebooks on desktop no longer
sync with OneDrive. As a work around, you may try
OneNote 2016. After finishing installing OneNote 2016, it should be automatically associated with your currently activated license of Microsoft Office 2010 and work as OneNote 2016 Home and Student.
When there is any updates, we could share with each other. Thanks for your understanding.
Best Regards,
Emily
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