The first thing to check would be the wiring from the main panel to the keypad. Remove the keypad and isolate the wiring between this keypad and the main panel. Then use a short length of new cable to temporarily connect the keypad back up again to the main panel and perform a test run to see if panel now illuminates and all functions are working. If you find the keypad is illuminating with this test set up, you need to concentrate on the wiring that you originally installed and find where it went wrong/got damaged/connections loose etc etc..
Easier to run a fresh wire and start again if not too difficult.
If the short test run still has the same fault, then I'd return the keypad for a warrenty replacement or at least speak to the manufacturer's technical helpline for expert advice.
There maybe a programmable setting to deactivate the backlights, but I can't find any reference to it and I'd have thought you would have studied the installation manual before asking this question, so don't think it will be that easy!
If you do find the fault, let us know with the add answer button to help others in future
Rupert
December 2019