Blue light comes on briefly, then a click and it goes off

My son's Nintendo 3DS XL doesn't turn on. When I press the power button, the blue light comes on for a few seconds, then I hear a click and it goes off. Both screens remain black.

Holding down the power button produces the same result. Plugging it into the charger doesn't help.

I've done some Googling and have read different things, but I'm not sure which of them applies to this problem. Thanks.