Yes, I'd imagined bad joints would lead to erratic performance, not death. I tried jiggling the plug around a bit, didn't help. I pulled the panel PCB and checked the power switch, which works, but it only gets 0.06 V

There is a yellow-rimmed coin cell labelled 5 V, and it only gives off 3 V. It's soldered to the control board and I don't have a proper electronics workstation at home so I'll have to take it to the university, but it's worth checking out.