Thanks again for the tips guys, much appreciated. Thinking along these lines:
Keyboard disconnected just in case
Volume buttons checked out ok (20k open resistance, they short to earth when activated)
Pressed down on various ICs whilst resetting in case it was a dry joint
Nothing - always this USB Downloader mode.
If the previous owner was *trying* to break it, I'd assume that it was a software fault and recoverable. As this happened at random, and there are reports of "intermittent I think I'm a cabbage" Kindles on Google, I think it's just dead hardware and am going to treat it like an expensive replacement screen/spares package.
I'll borrow the good screen for now and keep the spares in the drawer, just in case the serial turns up and is useful as a trade-in against a replacement at Amazon or similar - their CS rep on the telephone suggested that even if purchased secondhand and out of warranty, provided that you are the legitimate owner they'll knock something off a new one.
uriziel01 - feel free to take over the thread! I'm curious, but not quite *that* curious. (and I think I'd be wasting my time if the hardware were dead)