I have a similar issue, any cable can be replaced with a good soldering iron, solder , flux & shrink wrap and same gauge of cable on the headset .
these faults are caused by flexing of cable over time creating breaks in the cores.
my device not powering up at all , just waiting a working model to verify the fault then I’ll attempt a replacement cable.
a digital multimeter is also handy tool to resistance test the cores between the plug , in-line module and motherboard . Will tell you if it’s open or closed circuit . Open is broken core. It will also tell you if you have power at each point.
cheers
Daniel