1986ew

Hi, Ive been having trouble with my 2011 f150 5.0 not starting. When I turn the key the engines doesn't crank and I get a single click. All the electronics turn on including the blower. The click sounds like its coming from behind the glove box on the passenger side. The problem started about a month ago and would happen intermittently. At first I would have to turn the key a few times to get the truck to start. Then it wouldn't start for a day or two at a time. Now I haven't been able to start the truck for five days. I was able to pull the code "P0705 TRANSMISSION RANGE SENSOR CIRCUIT MALFUNCTION (PRNDL Input)". I looked it up online and the symptoms say it can cause a no start condition. I had the battery tested at auto zone and they said it was fine. I thought it was the starter before I pulled the code. Apparently the sensor is located inside the transmission, or I would have just swapped it out. Anyone familiar with this problem? The mechanic at the ford dealership wasn't familiar with the issue and they can't get my truck in there for 10 days. Im worried it could be an electrical problem and not the sensor, because the reverse camera stopped working a couple weeks ago too. When I put the truck in reverse the camera in the rear view mirror shows a blue screen for a few seconds then shuts off. Is it possible these issues are connected? Any advice? Thanks!