Toyota Prius Won't Start, P position malfunction warning

We have a 2011 Toyota Prius with 294k miles. Yesterday after driving the car with the usual starts and stops, the car wouldn't startup again. The instrument display was dead. We jump-started the battery as per owner manual instructions. We used the emergency start up procedure and the car started. After driving the car for 45 minutes to recharge the battery more fully, we parked it and powered down the vehicle. We attempted to restart the car again but it wouldn't start and the display was dead. We repeated the previous procedure using emergency instructions and the car restarted. However, the instrument panel then displayed a P position malfunction warning light. The car drives normally but after shut down it can't be restarted. We can't start the car normally at all, it must be jump-started to drive it. The P position malfunction warning light appears every time. I know this sounds like a failing battery condition but what does the warning light have to do with a failing battery? The battery indicator on the display isn't showing a bad battery condition. Please help with this phenomenon. Thanks!

 

Thanks for your reply. I have a strong feeling your answer is correct.

 

It was exactly as you said it was. The car works again. Thank you!