Thanks for the idea.
Unfortunately, the unit is still dead. While I was trying another bunch of hard resets, the screen ended up half dark, half white.
The update seems to work - the software recognises the 500 and goes through the motions, but no way does it resolve the issue.
Very frustrating. I've always babied it, and it dies like this.
I'm attaching a picture in case anyone wants to see what a dead PRS-500 looks like.
I'm probably going to get a Kindle2 or DX. Maybe they're made a bit better.