Screen dark except when brightness is stepped off of zero As shown in this video, the screen is dark, except at the few first steps when the brightness is moved just out of zero.

The notebook works otherwise perfectly fine. The image on the external monitor is fine.

Have you seen this before or can guess what the culprit is?
Yes. A loose cable, loose cable to LCD panel connection, bad inverter, failing backlight, power supply/voltage regulation issues inside the Mac all can cause what you observe as a symptom for brightness jumping and not working.

If you gently and slowly open and close the lid, most loose connections can be made better or worse. The powering it off and then seeing a little moment of light when you initially turn on the backlight circuit seems to indicate a power / inverter issue, but that could still be the bulb or bad luck/timing with a cable jostling, too.