Maxima 2012 Radio Is Going Haywire

5 days ago my car's battery was dead in the morning. I jumped the battery
and the car ran just fine all day. I didn't notice any problems with any controls
or the engine. The next day the battery was dead again and returned to
normal after the car was jumped. When I turned the car off for the last time
that day, I notice that the control screen for my radio and climate control did
not turn off even though the radio and climate were turned off as was the car.
I tried to turn the screen off through the settings and even though it was
switched to off the screen still continued to be lit up. On the third day, the
battery was dead again. I jump started the car and now the screen for the
radio was off at the start of the day. After two trips, the radio screen turned
back on after the third start and stayed on regardless is the car was running
or not and turning the radio and climate control off had no impact. I just got
back from the dealer. They said they couldn't figure out what was wrong with
the radio which they said controlled the screen. They said it wasn't a
programming issue. They said something was broken in my radio and want
to replace the entire unit for $2,100. What action would you recommend
next?