the lcd is an internal function of the radio... what I mean is if the LCD quits functioning, it is the radio that turns it on, not an external circuit in the vehicle. Obviously if the entire radio shuts off it may be a power supply concern, but if you have power to the radio (indicated by lighting turning on and noise from speakers, and button function) the radio has failed...
I had one recently, same problem, the customer seemed to have been told it was "a video cable" so he didnt appreciate my "needs a REDICULOUSLY EXPENSIVE radio" diagnosis and told me I was wrong... oh well, my REC will be playing music on the way home
Funny thing about that one was I looked in history and for some reason unknown to all the writing staff and other techs I asked, the tech number on the "previous video cable problem" diagnosis was a lube tech who didnt even work at the dealership any longer, I think
this diagnosis was for a reverse camera issue that he assumed just progressed to the lcd not working all together.