Prius 2014 Not Starting

First time poster here. Having a problem with my 2014 Prius that I'm desperate to solve. I purchased the Prius about five years ago and started experiencing this problem perhaps two years ago. Basically, when I press the start button, all the dash lights come on, but only a thin line square appears around the P (park) on the dashboard, and the car cannot be shifted into start. It just beeps when you shift. When the car is functioning properly a thick, broad square appears around the P. When this glitch occurs it takes multiple efforts, sometimes up to 20, to start the car. I just keep turning it off and on until the proper light around the park signal shows up indicating that the car will go into drive. This tends to happen intermittently, but gets worse over time. The problem is, I've taken the car in for diagnostics 4 times. Twice to the dealership and twice to another mechanic. Though they too will experience the issue, no codes ever show up indicating any problem with the car. It sure seems like a drain to me, but they can't seem to find any evidence of a drain. We've gotten new fob batteries to rule that out. The one thing they've noticed is the erratic behavior of the 12v battery. It will test out perfect one day but not the next day, and jumping it does solve the issue....for a few days. Though I strongly believe the issue with the 12v is a symptom and not a cause, it's the only possible explanation any of the mechanics who have looked at our Prius have been able to suggest. As a result, we have had our 12v changed out twice (we're on our 3'rd). Each time, the Prius will start perfectly....for a time, and then the same behavior will start up again. We just changed the 12v maybe 5 weeks ago, and yesterday the starting issue resurfaced. We're just at wits end. I have very limited knowledge about cars. We have a problem that numerous mechanics have seen for themselves, but are completely baffled as to the cause. And again, no codes ever come up in diagnostics. Any help here would be greatly, greatly appreciated! Thank you!

 

We do drive it a lot, so I'd be surprised if that's the issue. What would be draining the car when it's off?