Nope. Never resolved. I think the answer lies in a mosfet blowing. But without the schematics it is very difficult to tell. I've tested all the resistors and fuses on the boards that I have and they all seem to be conductive, although of course without schematics I cannot tell whether there are any that are partially failed and therefore at the wrong value. If anyone has copies of the schematics online I can test further.
Curiously I have replaced the motherboard with a known good variant and it is still refusing to turn on. Two different screens and two different motherboards. The only commonality is the power switch and the battery. Battery appears to charge adequately. So I assume it is functional. Very odd.