Intermittent trouble starting

First I'd like to start out by saying I have searched for this topic. It appears many others have had this issue, and I have not come across a thread in which a conclusion was reached. Some have reported a resolution with a new battery, or adjusting the brake pedal sensor, other have not had anything fix it. Just posting this here incase there was anything I missed (there was a LOT to read), or if anyone had this issue recently and figured out a solution:

Since I first bought my 2011 Prius III (second hand) I have occassional problems where I will depress the brake, the start button will turn green, but pressing it will not put it in to ready mode. All the electronics will come on (to the same extent as if the start was pressed twice w/o the brake being depressed), but that's it.

Information I have:
Seems to occur most frequently during the winter, but also happens during the summer, and after driving when the car is warmed up. Seems entirely random. Also, in the winter, it doesn't happen more frequently when it's extremely cold (less than 25deg) than it does on warmer days. So I'm not convinced it's temperature related.

I have always been able to eventually start the car. If I turn it on (but not ready) and wait 5-10 minutes, then it will start normally. I've never had to wait longer than that. Sometimes it will start after a minute or two, but normally takes about 5+. Sometimes it will start with the car off, if I wait a few minutes and try again, but the most reliable way to make it work is to have the electronics on.

Things that don't work:

*Pressing start again will either make no different, or shut the car off.
*Depressing the brake pedal and pressing start repeatedly, or in rapid succession will not work.
*Resetting the parking brake makes no difference
*Pressing the brake lightly, moderately, all the way, etc, makes no difference
*Holding the start button makes no difference
*Attempting to jump the battery from under the hood, or through the trunk makes no difference
*Turning off all the electronics in the vehicle (dome light, radio, fan, etc) makes no difference
*Time of day, driving pattern, etc make no difference. It will happen whether the car has been sitting overnight (most common) or if the car has been recently driven (less common). I have been stuck at fuel pumps a few times under these circumstances.

Things I believe I have ruled out:

*I have tested the battery after sitting overnight and it reads 12.5V. Some people have reported this issue resolved with a new battery. However, the voltage reading, combined with the fact that this hasn't gotten worse or more frequent over the past 2 years makes me think the battery is not the problem. Also, attaching a jumper battery does not resolve the issue.

*The brake pedal will ALWAYS make the start button turn green when any pressure is exerted. The amount the pedal is depressed doesn't resolve the issue, so I do not believe it is the position sensor.

*No CEL, funny noises, etc. Car has had regular, appropriate maintenance.

As mentioned, the problem is infrequent. Maybe a few times each summer, perhaps 6-12 times each winter (I drive multiple times a day). Won't kill me if it keeps up, but it bothers me that it keeps wasting time. Also, don't want it to be a symptom of a bigger issue that I'm ignoring.

Thank you.

 

I have disconnected my battery in that manner to complete unrelated repairs. I don't believe it made a difference. Recently disconnected the battery to replace my front door actuators. I had this problem occur once about a week later. Thanks for the suggestion, though, it wasn't a bad idea.

 

Update: It's been a while, and I have no answer, but some new information. I've had the car for over 3 years now, and the issue has persisted. It appears to happen more frequently in the winter than the summer. This winter, the battery started to actually die. Three times I've come out to the car to find it unresponsive. After the second time, I removed the battery and put it on a trickle charger overnight in my house. Even fully charged, the car still had this issue literally the first time I tried to start it after putting the battery back in (and the car without power for 12+ hours). After the battery died the third time, a few weeks later, I finally bit the bullet and bought a new battery. Now, with a *completely new battery* the car still has this problem. Granted, I've never not been able to start it eventually (not counting the times the battery was actually dead). It just sometimes has to sit a few minutes before I try again and the ready light comes on. So, while I have no answers, I can personally attest to the fact that (in some cases) the failure of the ready light to come on is not battery related. I had suspected this before, but now find the evidence to be conclusive. Just wanted to add this comment for anyone else dealing with this mystery before they chuck a perfectly good car battery to try and solve the issue.