This problem is extremely annoying: sometimes, the Start menu in Windows 10 will outright stop working. It won't appear when the Start button is clicked or the Windows Key is pressed. In addition, various Windows 10-style windows (such as the system's volume control that appears in the top-left of the screen when the volume is changed) will also not appear. Right-clicking on the Start button will then cause any 10-style windows to then draw... it's all very weird.
After many months, it seems I may have stumbled upon a fix for the issue. Every time I tried restarting or shutting down the system, Windows always complained about there being a task that wouldn't exit. The string given is:
Microsoft\windows\plug and play\device install reboot required
Microsoft introduced a "feature" that allows Windows to finish installing device drivers after an update or restart. Awesomely - it doesn't work. This broken feature has been the cause of months of (random) frustration and re-installations.
Anyway - whatever, onto the fix. Hopefully it's the fix; I haven't ran into the Start issue since.
To do this using the Start menu (eg. you're performing this as a preventative measure), just type Settings into the Start menu and open the item that appears.
If you have a broken Start menu, you can either click on this link right here or press Windows Key+R to open the Run window and then type the following, followed by pressing the Enter key.
ms-settings:
Include the trailing colon character otherwise you'll get an error.
In the Settings window that appears, click on Accounts (the little round guy; second row in the second column in my particular version).
On the left, click on Sign-in Options.
Scroll down in the view on the right and under the Privacy heading, uncheck the Use my sign-in info to automatically finish setting up my device after an update or restart.
That should be it.