Battery Charging AC Adaptor not working???

The Power Switch on my (brand new) Nikon P6000 should (according to the manual) blink when I plug in the AC Adaptor to charge the battery. But it doesn't. Nor did the battery charge fully when left on charge all night.

Can anyone suggest what's going wrong here?

also...

The battery has now been in a separate (Nikon) battery charger for over 5 hours and the light on the charger is still glowing yellow/amber.

Should this light go green when the battery is fully charged?

I've come from a line of Canon IXii, this is my first Nikon.

(The menus are a bit clunky)

I don't have a P6000, but the battery charger looks like the other Nikon battery chargers that I have. The orange light blinks when charging the battery and stays alight constantly when the battery is charged.

As for charging the battery in the camera via the USB cable - I suppose the voltage of the USB cable might be lower than the battery charger. You might not be able to get a full charge this way. But I don't know.