The first thing to do was to power up the problem speaker and try to find all the symptoms of the problem. The seller had told me that it wouldn't turn on when plugged in, so I figured I probably could plug it in safely without risking any further damage. 

Upon plugging the speaker in to 240V (the rated voltage), I was thankfully not greeted by any magic smoke. However, I was a little disappointed to see that the JBL logo on the front dimly lit up. This meant that the problem couldn't be as simple as a blown fuse or loose PSU connection. This was also where having the working speaker started helping to narrow down the issue. When plugged in up, the functional speaker starts with the JBL logo dimly lit for a split second, then brightly lit while the VU meter and button LEDs show an animated test pattern, then goes back to dimly lit until the speaker is woken up with the power button or IR remote. The broken speaker's JBL logo never progressed from the dimly lit state, and was completely unresponsive to button presses or the factory reset procedure with the DIP switches on the rear panel.

I popped open the busted speaker and was quite impressed by the internals, having only disassembled consumer speakers in the past. The whole back panel is a hefty cast aluminum heatsink with the port integrated. The interior of the speaker was lined with acoustic padding and all cables were wrapped with anti-vibration foam. I was surprised to find that despite the fancy DSP features and digital audio input, the power amplifier stage is old-school class AB fed by a toroidal transformer. That explains how each speaker weighs 12kg!

The signal chain is split into two helpfully labelled boards: The smaller digital board, with ribbon cables to the front panel (disconnected in the photos) and to the analog board, and the analog board with the PSU and power amp section and all of the rear-panel IO (analog audio, digital audio, USB, control).