I've tried compatibility modes on all .exe files and safe mode. Honestly, I don't know what to try anymore, I'm not too familiar with launching older games on new systems.

I don't get a black screen nor any processes in the task manager. As I've installed the game through GOG Galaxy, only the "Play" button goes gray for a bit then goes back to green.

If relevant, my specs are:
CPU - Ryzen 3 2200G
GPU - GeForce GTX 1060
RAM - 16GB

Same stuff for me. I suppose it is somehow connected with GPU or graphics driver, since I have GTX 1060 too.

Strange, I have a GTX 1060 as well and I run it fine.

Which driver version do you use?

GeForce Game Ready Driver version 417.71, the latest one.

Try and see if you have to manually install DirectX 9.0c.