Black screen (no backlight?) after LCD replacement.

There is no schematic available for the iPad mini 4. The only way to do board level work on this model is to compare to the other mini’s and the Air’s and infer functionality based on similar design. You’ll need to be patient and jump around from one schematic and board view to another. ZXW at least has the connections mapped out for the mini 4 but no other information.

The linked video shows pretty clearly where the backlight filter is. Probe it and see if it is showing continuity and then probe it in diode mode to see if the circuit is giving a decent reading (~.325). On the LCD connector (smaller one), the Anode pin is the 12th pin from the left on the bottom side of the connector (assuming the short connector is at the top of your field of view and the long one is at the bottom). The three pins to the left and three to the right are the cathode return pins. Start with that and try to determine if there is anything obviously wrong.