Here is a link to the service manual for your keyboard. It contains complete circuit wiring diagrams. As best as I can see, the LCD display backlight is fed by a +5V DC supply connection. Looking at the circuit there appears to be two (2) cable connections to the display. One is for data and screen settings (which has 19 wires) and the other is a two wire cable supplying the backlight (+5V and Eth).
There is a link connection JC1.0 where +5VD1 connects to +5VD2. It is +5VD2 that is the designated supply for the backlight. (shown on PSR-A2000 OVERALL CIRCUIT DIAGRAM 1/6 (DML 1/2) at point C2)
Here are images to show the salient points.
It may be that the +5V is missing due to a faulty connection, the Eth is missing for the same reason or that the backlight itself may be faulty.
Hopefully this is of some help.