Hi I've got the same problem, my macbook has had it for a while. Same thing with changing the brightness making it go on. From what I've read this is not the common inverter problem that people often have and neither is it the inverter cable because moving the screen makes no difference.
When I do get my screen to light up for a bit, I can often see a red/pink hue to it. This sometimes goes away after a while of the screen being on. But apparently the red colour of the screen means that there is a problem with the CCFL backlight bulb:
"Defective CCFL backlight may have the following symptoms: Screen flashes on red/pink and goes off. Picture stays on in red and slowly be come normal. Picture flickering with dim display. Picture flickering on and off. All these symptoms indicate that the LCD backlight lamp (CCFL Lamp) has reached the end of its life."
So in my case I know 100% that the backlight is faulty so I've bought another LCD display off eBay and hopefully this will solve the problem.
I can't see a red colour on your screen in the video, but it still is possible that the backlight is faulty, so don't rule it out.
Hope this has helped a bit.