Path to exit PSX Final Doom level 14, System Control:

You begin at the south end of the map.  Walk out the door
and continue straight (north) through the next room, and
follow the short hallway as it curves around to the right.
As you emerge into the room at the end of the hallway, turn
left and look for a switch on the wall.  Activate it, and
some stairs will begin to rise along the south wall of this
room.
Walk up the stairs, and look for the "EXIT" door, which is
located at the northwest corner of the room.
As you step under the "EXIT" sign above this door, a wall
panel opens behind you, creating a doorway in the southeast
corner of the room (just to the right of a long window).
Quickly run out through this new doorway before it closes
up again.
Walk down the short flight of steps beyond the doorway, and
you'll be in a small courtyard at the northeast corner of
the map.
Go to the northwest corner of the courtyard, and Activate
the switch you'll find there.
Go back up the steps, and the wall panel will open again as
you approach.  Step through, back to the room you were in a
moment ago.
Go back down the stairs along the south wall of this room,
and go west into the short curving hallway.
A wall panel has opened in the northwest corner of the room
at the south end of the hallway, revealing a small alcove
where 1 or 2 chaingunners wait to ambush you.
You'll find the blue keycard in another new alcove in the
southeast corner of the room, just to the left of a metal
door; Grab it.
Now go back to the "EXIT" door, and open it to reveal a
small chamber.
On one wall of the chamber is a switch.  When Activated,
the floor of the chamber drops down into a larger room
below, where some monsters await.
When you enter this larger room, you'll see a switch on the
west wall, and some vertical bars to the right, blocking
access to the north end of the room.
Activate the switch to raise the bars, and go to the north
end of the room, where you'll find the Exit switch.