So:
The taskbar in general is working - you can open Task Manager.
Clicking on the Start button at the left hand end of the taskbar does nothing.
The "Windows" button on the keyboard does nothing.
Have you tried the old-fashioned way of getting the start menu - Control-Esc ?
If there's still no joy, try a clean restart. You can do this from Task Manager. Click on "More Details" at the bottom, then the File menu of the fresh view should have Run New Task. Enter
shutdown /r
Tick the box for Admin Privileges and click OK.
Windows should then perform the same actions as if you had selected Restart from the Start menu.
Note that Restart does more in the way of initialising things than a normal Shutdown followed by switching on with the power button.