With the computer asleep or shut down the orange battery charging indicator light flickers.
The laptop will not start up unless mains power adaptor is connected and switched on. It appears to function normally then but the battery state icon popup in the system tray says "Power connected, battery NOT charging". The level in the battery is indeed declining. The charge indicator light is now flashing steadily with a frequency a little more than 1Hz. Unplugging the charger makes the little plug on the icon go away but no difference to the charge indicator light.
This happened after I got a message from Asus telling me that I needed to ugrape the BIOS which, like a fool, I did!