Go upstairs to the north, and flip both switches. Walk back down, and go through the next four doors to the west. Head to the northern room, and go under the arch to be teleported to the platform behind it. Grab the red key, jump down, and head to the now revealed southern door. Open it, and use the eastern computer. This will cause one of the bookshelves to the south to lower; grab the blue key, and backtrack to the start of the level. Open the blue door to the south, and walk in. Wait until the wall has lowered, and go east across the boardwalk. At the end, grab the box of shells and box of rockets (or at least walk into where they sit,) and the northern wall will lower. Grab the yellow key at the bottom of the stairway, and return to the beginning of the map. Go through the yellow door to the east, hit the switch nearby, and go through the eastern teleporter before the wall rises again. Press the next switch.
Other points of interest
In the red key room, step onto the eastern platform with a rocket on it. You will be taken to a platform with a super shotgun and a plasma rifle. (sector 20) Step off the platform to return to the red key room.
In the blue key room, use the computer to the northwest to lower the nearby mainframe, upon which there are a rocket, a box of rockets, and a bulk cell. Doing this will also reveal an outdoors area (sector 87) to the north, where you can obtain a rocket, a bulk cell, and a box of shells.
After grabbing the blue key, remain on the lift it is on until it rises again. After this, jump to the bookshelf to its south to grab a rocket launcher. (sector 78)
In the final room of the level, one stone wall near the yellow door is covered in grime. Press on it to reveal a secret room with a lift. (sector 56)
Take the lift in secret #4 up to the wooden door, and open it to find a soul sphere. (sector 16)