HINT
(It is recommended to read just up to the point you're stuck at, and not continue until the end of the hint):
To open Door Four, give the book 'The Catcher in the Rye' (from the Library) to the man in the room which can be accessed from one screen south to the Lobby.
Then, give the video cassette (Get it from a room one screen west to the TV room screen) to the man in the TV room, the most south-eastern room of the building.
