In order to get this game series working on my Windows 10 computer, I needed to add:

dinput8.dll

...to the game's folder. I had to search for it online. Before I did, the program wouldn't start, at all. Compatibility mode didn't fix it. This DirectInput file seems to be a common fix for some games designed for Windows 7 that won't play on 8 and newer.

I don't know if GOG or the publisher could add this file into the game's directory by default, but wanted to share this in case anyone else is having an issue with the game not starting.