Hello,
What you also can do is uninstall Office 2010, reboot and then reinstall it.
There is also a possibility that some other updater (non-Microsoft) causes the hang.
Let's try something like this:
Please close the Windows Update interface (if opened) and start PowerShell as an administrator (as mentioned in previous posts) and enter:
Stop-Service wuauserv
Stop-Service msiserver
Stop-Process -Name msiexec -Force
and THEN start to install the downloaded MS Office 2010 OneNote update. The first command will stop Windows Update service. To re-run it - simply reboot the computer.
I believe we need to understand what other installation is "in progress". I fear is that after you uninstall MS Office 2010 (to either install Office 365 or reinstall Office 2010) you won't be able to install it
because there will be some "other installation running".
I do wonder how deep you wish to go? There are programs like
Process Monitor that will show most of the things that are running on the system at a given time. The log from the program can be saved (it can take 200 - 500 MB of space) and then uploaded to Dropbox for analysis. You could start Process Monitor, wait
for the issue to resurface, stop the trace, save (File -> Save -> All Events) and sent it to Dropbox. I'm not sure if you would be comfortable to do so or if you need more detailed instructions? The problem is to start Process Monitor at a specific time to
capture the event of "pending install".
There is also a possibility to use a software like TeamViewer so you could share your desktop screen. However, that would require to take our conversation outside of this forum (which would require one of us to disclose e-mail which
is a bad idea on a public forum).