Unless manufacturers started adding circuitry onto the backlight and added an extra pin to the connector, there would be no way to test the backlight. An extra pin and specific circuitry would be needed as well, to test the inverter.
No way for software to test this. All the computer would be able to do is report if it is plugged in or not, which it typically does in the form of an LED. There isn't any way to logically implement this.
Really, this is the only feasbile thing that a post card could test for, but so many laptops have embedded graphics, that the utility of a POST card is questionable.
Again, no real way to test this without additional circuitry. Even then, the only thing that the computer would report would be whether or not it's receiving power to the board, not whether the power is actually getting to the board.