These can be completed in any order. To kill the Stingons just shoot them as soon as you encounter them. Access the computer by disabling the camera (with your gun), claiming to be Mick Annick, and entering the security code which you can find in a cup on the upper levels. Disable the engines with the acid that you find in the lab.
Part 2: The Hidden Base
Escape from the prison by picking up the rock and throwing it at the gun. Then shoot a hole in the wall.
Find the stick and retrieve the tooth from the cave with it.
Cut the wires according to the colours shown on the display screen.
Shoot a hole in the hatch.
Talk to the Stingon, take the screwdriver. Take a radio. Take the power pack from the laser using the screwdriver. Use the power pack on the radio.
Place the radio on the door control. Leave by the lift rather than the main exit.
Take the drill and return to the lift.
Operate the door control to get the radio, and play back the recording.
Operate the subspace radio.
Make your way to the surface and use the drill on the door.