It seems there is no one solution to this issue as i've read at least 10 different posts before I figured out a fix that worked for me by myself. Hopefully this will work for you.

1. Go to the folder your game installed to. (This is usually "C:\ Gog Games\The Longest Journey" But I've seen others so if it's not there for you just right click the shortcut and click go to file location.

2. Open the file "Preferences.Ini"

3 Under the section headed by [DIRECTX] you will see one of the commands listed as "bool_UseHardware=0". Change this to "bool_UseHardware=1" then save the changes to the file.

4. Relaunch game and enjoy.

Hope this helps :D