You have to do a speed run of the game up to the point where you get the 'Unusual Key (no more than five minutes can be spent up to this point). When you have the key, go back to the 'real' dimension, and open up your father's office door. Then, open up the central drawer, and you will hear a switch click (if it says 'If only I'd have got here sooner' it means you were too slow, so you have to restart and try again). This switch will unlock a door in the other dimension. So go back to the other dimension and open up the door that is equivalent to your dad's room.

This room is very interesting. (I won't spoil what it contains, find out for yourself) and then there is a computer screen where you can enter a password. If you've played through before (endings 1 and 2) you should be able to figure out the password, but if not, the password is Makers . Not sure if capitalisation matters but it 100% works with the capitalisation I just gave.
When you've entered the room and put the password in, go to the basement room (don't actually go down into the basement, just click on the room to the right of the clock-puzzle one time), and then click on the north-west part of your screen to find a secret door. Go out the door to end the game.

I made a video of this years ago when Without Escape was on the Xbox 360, however since the Steam version is slightly different from the old 360 version, the video may look confusing, but the method to get the secret ending is the same.

Video here: