Hi. It's not good news unfortunately.
It's usually assumed that a dim screen has either a dead inverter (most common) or a blown backlight bulb, but just once in a while, it goes like yours has, and the mainboard is at fault....
Your mainboard isn't sending power to the inverter (12v goes in, and then the inverter, well it inverts :) and makes the 12volts into 700-1000volts depending on laptop model. This is completely separate from the actual screen/picture circuit, that's why it's fine on an external screen. The only bit you've lost is the initial power to the screens bulb(s).
It's worth carefully checking the full wiring from the mainboard to the inverter just in case it has a break in, but most likely that a part of the mainboard needs an SMD level repair by a professional who completely understands how the circuit works.
It's usually very expensive to replace the full mainboard on any MAC :(
If you decide to check the inverter is getting it's power, please only do so if you're completely familiar with electronics and high voltage stuff, as the inverter can hurt/kill when touched.
Hope that helps in some way.