I did a fresh install of Duke Nukem 3D and also installed the high res pack. I now have the original DUKE3D.EXE and eduke32.exe in the folder. I've tried starting with both. Using the Gog shortcut to start the game, it begins with music but then just drops to the desktop with no error message. Using eduke32, it mentions not finding an eduke.cfg so it asks to use the duke3d.cfg. I also check "enable autoload folder" (also tried without selecting this) and tried with and without "custom game content directory" as None and also selecting DOSBOX. Eduke32 doesn't do much, just the box that pops up and tells me it's stopped working.
I selected both exe files to run as admin and the game is in C:\GOG Games\Duke Nukem 3D. I have Windows 10. I saw a post about changing to OpenGL but I don't have any kind of graphics setup in the directory.