Hello, i have PR1 and windows 10 and when i launch the game i have intro and no problem.
After that i got the game menu and i can see only the first 3 options the other is hidden with black screen.

It may be that you just have to adjust the resolution.

I don't know if it will fix your problem, but you could try a solution I posted about running it in windowed mode as a workaround (you won't be able to watch the intro movie, but you will be able to play the game):

https://www.gog.com/forum/port_royale_series/how_to_run_port_royale_1_in_windowed_mode_on_windows_10_and_fix_for_fast_scrolling

same here...

Doc from the amazing gog support showed me some tips and it kinda worked for me, at least so far:

Please follow these steps:
1) Please add GOG GALAXY folders:
C:\Program Files (x86)\GOG GALAXY

C:\ProgramData\GOG.com
to all of your security (antivirus, antyspyware, firewall) software exceptions list. If the game is installed outside of GOG GALAXY folder, then please add game's installation folder to security software exceptions list as well. Once above is done, please select the game in GOG GALAXY, click on Customize -> Manage Installation -> Verify/Repair.
https://imgur.com/mPXqg0n

2) Reinstall the June 2010 DirectX runtime package. You can find the archive file containing the 2010 package installation files here:
https://files.gog.com/support/Directx_Jun2010_redist.exe
You will have to extract the files into some folder, then open that folder and launch the DXSETUP.exe file in order to proceed with the installation.

Please have in mind that this will only add DirectX 9.0c to available pool of DirectX libraries, and it will not overwrite your other versions. Some games are not able to utilize newer DirectX libraries, and they require DirectX 9.0c.

3) Please update your graphics device drivers:
https://support.amd.com/download (my card's a radeon one)

check my attachments for settings et al and here, too

https://imgur.com/BnMeW6Z

and my directx settings here!!

https://i.imgur.com/rpuexem.png