Did you forget to unplug the battery?
Backlight failure is a very common issue on the 6s models in particular because of the 4V pin and the ground pin on the LCD connector being next to each other can can be shorted easily when connecting or disconnecting the screen with the battery plugged in (even with the phone and screen turned off).
Usually you will see a puff of smoke near the screen connector when this occurs.
To confirm backlight failure, turn the phone off and use a flashlight to see if you can see a dim apple logo on the middle of the screen, additionally you could connect the iPhone to a computer and open up iTunes to see if the phone successfully boots up and is detected by iTunes.
To get backlight circuit fixed, that requires someone to do micro-soldering on the phone (basically repairing the backlight circuit and components on the logic board).
I would estimate about $80-$150 for the job to be done.