It looks like this may be a lost cause :(

I've been running this on the mains, but today forgot to switch on at the wall.
The battery only lasted long enough for a brief flicker of the 'on' LED.
Also I've now discovered some of the keys aren't working.

Having said that, I do very much appreciate all the help you've given, and have
learned a lot more about modern laptops!

So, the next question is, can anyone suggest a reasonably inexpensive laptop
that plays well with Linux?