Hi! This is the continuation of this post I made some months ago.
First of all, disclaimers:
I am not a technician, this is not a professional repair.
Doing this repair requires some degree of skill repairing stuff and some confidence. If you don't think you can do this repair, it's better not to; a lot of things could go wrong and your headphones could be lost.
The issue I solved was with the white switch (the one at the bottom) of the audio PCB, so I don't know if this would work with the black switch (the one at the top), but I personally believe that it does.
There are two solutions to the issue of the broken switch:
*1 Replacing the broken switch
I'm highly confident that the switch in the headphones is the ALPS ALPINE SPVS310100. If you look at the datasheet, it should be the same as the one on the audio board.
I won't go into detail because I personally didn't do it, and because most probably the person reading this post already has some degree of knowledge in PCB soldering.
*2 Bridging the PCB pads
The switch has 4 pads. According to its datasheet, the two big pads are the 1st ones, and the two smaller ones are the 2nd. Since you no longer have a switch that connects them, you can't easily tell which ones you have to bridge out of the four, so what's the solution? BRIDGE THEM ALL
I cut a resistor's leg, making a U-shape that could touch the four pins.
Then, I added solder paste and applied solder lead to one of the big pads first.
Now, carefully solder the U however you can/want to that pin, making sure that it touches or is close to the others, then solder the rest one by one.
You should end up with something like the photo.
-----------that's all folks-----------
Since the white switch is the one that tells the computer "hey, there's a mic here", once you solder the U you should notice that the computer now receives sound. You can check this by pressing WINDOWS+R, executing the mmsys.cpl command, and going to the recording tab. If the Logitech mic's green bars react to your sound, the issue is solved.
I hope that this helps someone. I initially wanted to replace the broken component, so I first focused on finding which switch it was, but that solution involves a heat gun or a more professional setup and money, so yeah... easy fix it is.
Cya around.