Once you've dealt with the soldiers, get ready for a timed run. The right button (when facing them) opens the inner doors and closes the trapdoor above the pit in between the two sets of doors, allowing you to run over it. The doors stay open and the trapdoor closed for about 45 seconds. The left button opens the doors beyond the pit, which then stay open for about 20 seconds. So you'll need to open the inner door first, then the outer, and then run through before the timers run out. This sequence is detailed in the screenshots below and shown in this short video walkthrough.

Climb up to the right button (i.e., on the right catwalk when facing the entrance) and save the game if possible.

Press the button.

Then immediately press Look to cancel the cut scene showing the inner doors opening and the trapdoor closing.

Backflip off of the catwalk.

Roll and take a running jump angled slightly to the right in order to land on the computers in the middle of the room.

Run across the top of the computers and jump at the end to grab the other catwalk.

Pull up, turn right, and run forward to the left button.

Press the button.

Quickly press Look to cancel the cut scene showing the outer doors opening.

Then backflip off the catwalk.

Roll and run past the computers...

...and through the open doors.

NOTE: This method is quick but does involve losing a little health when you jump down from the catwalks. If that bothers you, try this alternative sequence: Press the right button, press Look, turn right and run along the catwalk, jumping at the end to land on the bank of computers. Run across the tops of the computers and jump to grab the other catwalk. Pull up, run to the other button, press it, press Look, and then run back along the catwalk, veering to the left at the end to land on the computer instead of the floor. Then run through the doors into the next room. I haven't shown screenshots for this sequence, but it's part of the video walkthrough.

[Part 1 | Return to the Area 51 Walkthrough]