Well, things have turned out well in the end:

I plugged it into the charger last night and reset it as it wouldn't shut down after removal from the sled. I left it plugged in to charge till this morning. It was showing a large battery icon again.

When I checked this morning, the large battery icon had gone, and the unit seemed to have shut down. I pressed the power button, and - wonder of wonders - it came back to life!!! Phew!

So I am really unsure of what has happened - but one thing is certain, it's time to RTFM, methinks.

Thanks for your help, guys.