Deleted BOTH Microsoft AC adaptor AND Microsoft ACPI-Compliant Control Method Battery
in Device Manager, rebooted, and - lo and behold - Composite Battery reappeared under
"System devices", along with the correct power icon behaviour :-)
I've seen dozens of Google references to this icon misbehaving in laptops and this
is the only fix that has worked. If the driver files themselves are missing, there's
a neat way of getting them back - see the post from DogHair (you couldn't make it
up !) here