Headset stopped working (assumed water damage)

Hi, I was wearing my headphones outside and it started raining, I continued in the rain until I got home. Headphones worked the entire time. Sometime after getting home, the headphones played the 'please charge headphones' chime and switched off. I thought nothing of this and still don't know if the battery was flat or maybe shorted.

After charging, the headphones would not turn on - the only observation was all LEDs on the left cup momentarily light when the power button is pressed.

I followed these instructions and found nothing obviously wrong visually: Sony MDR-1000X Noise Cancelling Headphone Teardown

I measured the voltage across the battery terminals as ~4.0V. And checked for a short between the +ve and -ve terminals on the board. This actually showed ~150kohms which surprised me, but as it was slowly rising I guessed that there was a capacitor across these terminals.

So far so normal, I don't know what I am doing and I have discovered nothing, pretty much what I was expecting. But then, when I put the battery back in, the headphones turned on, played the 'power on' chime and proceeded to play horrendous feedback through the speakers (probably because the mic was loose on the table). I used the power button to turn off the headphones, but then I could not turn them on again. I took the battery out and repeated what I had done but could not reproduce what had happened (turning on).

I went back into the left cup thinking maybe there is a short in the power button but have not found anything and am now stuck. Any advice is welcome.