Any luck on this? I'm guessing that it didn't turn out to be an issue with the wires somewhere coming loose?
The other thing that may have happened is one of the surface-mounted components on the circuit board may have come loose. Mind taking a picture of the circuit board and posting it? There are several transistors that, if they were damaged somehow, would explain why one system is working and another is not.
As for something getting shorted, that is totally possible. There isn't really one wire that drives audio/lights, the circuit board actually does a lot of this and so the problem is likely there if the wires going to the speaker look good.
I would pull apart the pen click system in the handle and make sure you got the small little components into the handle properly.
In that image you can see that the pen clicker is made up of the button, or cap, a white shaft with teeth at the end, and the mechanical inset that slots into the shaft that interacts with the teeth. The way those components are oriented in that picture are correct: If the tiny inset piece doesn't have the smaller portion inserted into the longer shaft, it won't work properly. Notice also that the cap screws into the shaft, and that, depending on how your trap turned out, having it screwed on too tight or too loosely can cause the pen mechanism to no longer function.
What is not pictured there is the actual head of the mechanism. This is the black thing that inserts into the opening at the end of the handle and actually pushes the tabs of the gate that controls the doors. When the button is pushed down, this is what is ultimately pushed down to close the doors. It needs to be seated properly into the opening on the handle to make sure it isn't out of reach of the pen clicker mechanism.
Finally, in the gear box that the door gears interface with, the springs on those tabs are what pushes the pen clicker assembly up when the doors open. If those springs are not on their pins, then the whole thing will stop working because nothing is putting tension on it all to keep the "pen clicker" working. Without the pressure from a spring, nothing interacts properly.
So, there are some thoughts. See if any of that helps figure out what may be going on, and if possible I would liketo see a picture of the underside of the circuit board with all the leads, transistors and resistors. Like this:
If that's too much to ask, then at least start with some of the other ideas and see if you can manage there. Also, when the screw dropped behind the circuit board, was the trap turned on?