The Longest Journey won't run on Windows 7
After some searching (too much, that's why I'm posting the answer here) I found a solution on the forum of Good Old Games.
Adding the following DirectX section to "preferences.ini" file located in "C:\Users\UserName\AppData\Roaming\The Longest Journey" seems to solve the issue:
[DirectX]
GfxDriver=display
int_BitDepth=32
bool_IsDoubleBuffer=0
bool_UseHardware=0
bool_StartFullscreen=1
bool_ForceSingleBuffer=1