Welcome to the forum, as far as the LED light on the radio it would be rare for these to go out not impossible, you can check the solder joints on the display by removing the radio with the key and on the rear there are some screws 4 or 5 I forget then pull the cover exposing the circuit board.
more likely it is a function of the radio that has failed suck as a stereo light not coming on may be a weak tuning capacitor, these radio electronics are getting old and need service.
Good luck.