With the items from the safe, return to the Tesla Trap, and below each Tesla Coil, there should be some rods that shoot electricity up to the top, with one missing on each. You can place the rods you acquired from the safe into these spots.
Now switch the generator from protect to destroy.
Now you must play a game of Simon Says at the computers you interacted with earlier, and at the computers at the rocket test site.
The way the game works is, after interacting with the computers, the four symbols will appear for a short time, and you must remember which monitor corresponds to which symbol. They will then disappear, and one of the symbols will appear on the large monitor.
Simply interact with the monitor corresponding to that symbol, and then a new one will appear. Repeat until the game ends, and one of the Tesla Coils will have a white glow. Now repeat this with the computers at the rocket test site. Be weary, as if the rocket begins testing during the game and you abandon it, you will have to restart the process on both computers.
With both coils charged, approach the Tesla Trap generator, and a button will now be glowing green, and you can interact with it.
The rocket holding Dempsey's pod will now be blown up, and it will fly down to the courtyard.