The Age of Empires II Scrolling Bug

That scrolling bug should be fixed by the community-made (non-official) AOE II: The Conquerors patch, UserPatch | https://userpatch.aiscripters.net/ :

This is a feature and bug-fix update for Age of Empires II: The Conquerors Expansion. Its primary focus is to correct several long existing issues with the AI system and related game elements.

Among many other fixes and improvements to AOE II: The Conquerors, one if its core features is:

Uncontrollable game view scrolling bug has been fixed

Notes: The UserPatch installer must be run with admin privileges in order for it to be able to install all of its fixes.

If you would like to simply enhance v1.0c, without upgrading to v1.1, you can hold the Ctrl key while clicking the Install button. This will block all v1.1 gameplay fixes, allowing for the use of v1.0c saved and recorded files. To do this via command line: SetupAoC.exe -c. Enhanced v1.0c mode is not recommended for normal gameplay. (Thanks to naxa for mentioning this.)

UserPatch installation guide

You tried shutting down all running processes and that didn't help. That zeros in on the running services.

Further, since you can uninterruptedly play AoK immediately after a fresh restart, but cannot when eventually that ScrewThingsUp flag is set to true, that means the service is set to Automatic (Delayed) Start mode (or even Manual mode, but the automatic one is more likely).

Sort your services by mode and run through all that are on Automatic (Delayed) mode. Stop non-essential services one-by-one and try running AoK after each stop. You should be able to find the rogue service.

If not, repeat the process with all Manual mode services that are currently running. Stop them, disable them, and test AoK.

Once you have zeroed in on one faulty service, permanently disable it (provided it is non-essential for any other task you perform).

I have made an important discovery. It isn't a solution to the actual problem, but it is a superior workaround compared to the full OS restart:

You don't have to restart the computer -- it is sufficient to log out [from your Windows account] and then log in again!

This I can live with. It will not even terminate important Windows services, such as the Windows Media Center Receiver Service that record TV programmes.