Where did you install the game? Tried Admin mode?

Hi! What error message are you getting?

try installing directx

Might have to change compatibility settings to XP or Windows 7.

I don't recall any trouble running the game. Maybe you might want to see if there's a graphical settings setup or command line operation you can do. Poking the engine.ini might let you set a resolution or windowed mode before you're in.

I installed it in the normal GoG folder.

Direct X is always installed and as i said, everything is installed and updated.

I also tried compability modes and admin mode.

No error message.

Just a black screen with the top left corner white.
can't end game with task-manager.
have to log out and in again or reboot in windows to close game.

You mean direct x 9.0c redistributable. Since people seem to forget that it's a different dx that needs to be installed to run old games,even though there is already a directx installed which is probably a new version.
But i think the OP maybe knows this. Oh also don't install games in program files just incase

exactly what I mean. I should have been more clear.

Install the game outside of "C:\Program Files (x86)" to something like "D:\Games\GOG". To do this, go to "Settings -> Downloads" and change your "Game installation folder".

Also, try to run the game using DxWnd.

I presume by "remake" you mean the 10th Anniversary Edition?

Have you tried these suggestions already?

https://www.gog.com/forum/the_settlers_series/settlers_2_10th_anniversary_black_screen_and_crash_to_desktop_on_startup

https://forums.ubi.com/showthread.php/484434-Settlers-2-10th-Anniversary-Edition-problem-Forums

Also, not sure if Event Viewer would say anything?

Since you are playing on a laptop, do you have two GPUs (like many have the Intel HD GPU, and then another NVidia GPU)? If so, are you able to check on which GPU the game is trying to run, and force it to either GPU (in order to see if it works better on either one)?