Okay, this is a little cheaky because it's for the disk version of Patrician 2 rather than the GOG but I can't find any other comunities so here's my problem.
When firing up the game it black screens instantly and shows no sign of working, force quitting the program starts the video player which plays the opening movie but once that plays through it quits to desktop. Does anyone have any suggestions?

The answer to this (for a CD version) is to right click on the shortcut icon for Patrician II, then select Properties. The field "target" should end: Patrician 2.exe". After the quote marks (") enter (with a space first) /nointro. Then click ok. on the bottom of the Properties box. The game should start fine then. I found this in the readme file for the game.