How do you get past the EULA screen?
I have tried keyboard keys, a controller and still no joy.
I am not daft, but what am I missing here?

You tried put the game in a window mode? i can use the arrows of keyboard with the windows screen, after press alt + enter.
Make Alt + Enter same for put the game in window mode.

Windowed mode is no joy either.
This is where it is stuck.

from googling around it seems there's a lot of people having this issue on every version (steam, gog ... )
Some people report some solutions , maybe one or all of them could work for you :

1 - find the game executable, right click on it then select "Properties", then click on the Compatibility tab
Then there check "Disable Fullscreen Optimisation"

2 - If you're running the game through galaxy, disable the galaxy overlay

3 - right click on your game shortcut, add
-nolegal
to the end of the "Target" line

this will allow to launch game without the EULA but apparently it will break the game own menu , but as read on a steam thread : good luck
If this work, remove the -nolegal from your shortcut after that, as the eula would have been accepted , but the -nolegal would continue to break the menu at further launch

How to fix the frozen "EULA" screen when launching the game:

1. Go to the folder where the game is installed.
2. Inside it, open the "1" folder, then "text", and then look for the "en" folder, which usually corresponds to the English language.
3. Inside the "en" folder, locate the file named "EULA.txt".
4. Open this file. If it is empty, type anything inside (for example, just a word or short phrase).
5. Save the file and then launch the game. This usually allows you to bypass the frozen "EULA" screen.

If it doesn’t work:

Instead of using the "en" folder, try opening the folder that corresponds to the language you believe the game is using (e.g., "pt", "es", "fr", etc.).

If it still doesn’t work, repeat the same procedure (writing something inside "EULA.txt") in all the folders inside "text" that contain language codes.

Direct from GOG Support. It fixed my issue

0) Please make sure that your Windows installation is most up to date.
 
1) Please open the GOG GALAXY App, select the game and use the repair button which will be located next to the PLAY button (on the right) > Manage installation > Repair
https://support.gog.com/hc/en-us/articles/360003930017-My-game-data-is-corrupt-How-can-I-repair-my-game-
 
2) Please install the June 2010 DirectX runtime package:
http://files.gog.com/support/Directx_Jun2010_redist.exe
or
https://www.microsoft.com/en-us/download/details.aspx?id=8109
 
The following video might be helpful:
https://www.youtube.com/watch?v=1LL8Hna3FIc
 
3) If you are using Nahimic, please could you disable this audio software or uninstall it completely as it has proven to be problematic with many games?
 
The article below might be helpful when it comes to disabling the Nahimic service:
https://support.gog.com/hc/en-us/articles/4408556606237
 
4) Please go to the game installation folder:
- If the game was installed via GOG GALAXY, please select the game in GOG GALAXY, click on the icon on the right side of the PLAY button -> Manage Installation -> Show Folder
- If the game was installed via offline installer, then you will have to manually navigate to the game installation folder, by default it's: C:\GOG Games\game-title\
 
Once in there find game's executable, right-click on it, and select Properties. In the properties window please switch to the Compatibility tab, and enable "Disable full screen optimization" and "Run as administrator". Press Ok to apply settings, and try to run the game again using the executable file.
https://support.gog.com/hc/article_attachments/360019085197/FullscreenOptimizations.gif
(You might want to close GOG GALAXY before performing this step).