I've got a message to GOG already sent, but I wanted to still pose this question.
I can't get the game to launch. I get the following message dialog that pops up in a box when I try to launch:
"Patrician 3: The resolution (800x600x16) could not be initialised. Please install the latest driver for your video card and then start the "P2Setup.exe" program."
I admit I haven't tried to update the graphic card driver, primarily because the game is older than the card. I also had run the test box repeatedly and tried to set the resolution to the max, but I still get this dialog box no matter what I do. Once you click "OK" the box closes and that's all that happens. It's very frustrating.
I can find no other setup options or other things I can change.
Thanks for any ideas.

Glad to hear GoG was able to solve the problem.

Yes I believe it is solved. Just giving it some time. Thank you for your efforts!

So does this game support any widescreen resolutions?

I quite agree. I'm seriously relunctant to mess around with the registry "by hand."

Please at least read the topic next time to see if your question is answered already. As I said earlier, game supports 800x600, 1024x768 and 1280x1024 resolutions so no WS support.

I have the same issue as the original poster. I have a ticket in with GOG since yesterday afternoon but I'd really like to play right now. Is the only fix for this issue the registry fix? Does anyone know the actual registry settings needed to make this work?

I had that same problem until I tried a couple of different things.
I opened up the Patrician3.exe file's Compatibility menu and poked around...
I set it to Windows XP SP2 compatibility and set it run as administrator.
I also switched DEP (Data Execution Protection) to only Microsoft essential services.
I am running in Win 7 and the game plays fine now....

Does GOG support take weekends off? I emailed Friday afternoon to get the registry file mentioned in the solution and have not received a reply yet.

I remember reading on these forums that this was the case, or at least that they have a lot fewer people working on weekends.

Yeah...that's great the initial poster got his problem solved. How about the rest of us that bought the game and can't launch it?
Even if you could just paste the content of the .reg file, that would be much appreciated. It's usually just a few lines of plain text.
EDIT: I found the solution by reading How To Run as Regular User

Thanks, Zwergner. Your post is the only one in this thread that solves the issue for someone other than the original poster. GOG support has proved to be 100% worthless in my scenario. They have yet to reply to my request from Friday. Thankfully I got the game to work, no thanks to GOG's slow/non existent support team.