Instructions
Remove the four screws on the back panel of the PS3 controller. Separate the two halves of the controller, being careful not to touch the circuit board.
Slide the shoulder button container away from the controller to expose the socket.
Remove the broken shoulder button by sliding it away from the controller and lifting it out of the socket.
Press the rubber pad in the shoulder button socket with your finger. If the switch underneath the pad clicks, continue to step 4. If the switch underneath the pad is already depressed or does not click when pressed, pull the rubber pad upward to reset the switch. Test the switch again by pressing the rubber pad with your finger. If the switch is still unresponsive, it may have broken off of the motherboard, and you will need to replace the controller.
Replace the shoulder button by sliding it straight into the socket. Push down on the button to snap it into place.
Slide the button container back into the controller panel. Press down on the shoulder button to test it. If the button pops up after being depressed, the switch and button have been reset properly.
Join the two halves of the controller panel and screw them together with the four screws. Make sure that the battery cable is not pinched by the controller panels during reassembly. Turn on your PS3 console and test the repaired shoulder button.