2010 Prius - Trouble starting / turning off - 12v battery needed?

I have a 2010 IV Prius that has been having the following issues starting up / turning off:

• On February 4th in the evening: car wouldn't start. Started on 5th try - showed "HYBRID SYSTEM OVERHEAT."

• On February 15th in the evening: car wouldn't start. During multiple attempts to start hybrid screen to the right of speedometer flickered / went in and out and was faint. Started on 5-6th try.

• On February 16th in the afternoon: car wouldn't start. Hybrid screen to the right of speedometer flickered and went in and out during startup attempts. Eventually car started at 5-6th try - but display to the right of speedometer did not come on at all. Car felt like it was running on engine only.

Took car to Toyota dealership - they had it for 2 weeks and could not figure out what the issue was. Car did not show any error codes. Said they did not experience issues either. Gave me the car back.

• On March 3rd, as soon as I got the car back and while still in the dealership parking lot, I pressed the start button with my foot on the brake and only the AC / radio came on. Called over service advisor and when he came tried it the car started up fine.
  
  
• On March 6th, same thing happened - AC / radio comes on but the car didn't start. Wouldn't turn off either - AC / radio ran but I was not able to turn them off or start the car. Eventually got the car to turn off. Happened twice in same day, recorded videos of it occurring and took car back to dealership.

March 7th - dealership calls and says the 12v battery is VERY low - never seen it that low. If I remember right, they said it should be at 100 cranking amps at the minimum but it's way way below that (I may be off on the numbers).

Apologizes for not checking on battery the first time they had the car in. Thinks this is possibly the cause of all my issues. Says they will waive some fees and give me a discount due to my patience and can get the battery replaced at $233 (including labor) before taxes.


My question is - could the battery have gone out while it was sitting on their lot in the 2 weeks? Is $233 a fair price?

 

That was the service advisor's first thought when I brought the car in the very first time, but after holding the car for 2 weeks they said it's OK.

 

Gotcha! Thanks for the suggestions. I did purchase the extended warranty as I got the car certified pre-owned in late July of 2014.

I'll give the go-ahead on the battery on Monday.

Can the 12v affect gas mileage as well? I've usually gotten around 40-45 (when I first got the car), 47 if I really watched it, but the past few days upon getting my car back I was getting 30-36mpg !

 

Thanks! Interesting info.

Yes, the $233 includes installation. My service advisor claimed the price was after pulling strings and applying discounts.

 

Got the battery replaced and so far so good. Mileage seems to be much better at the moment.

Just out of curiosity, has anyone's big battery ever charged all the way or does it usually show just one line short of being charged on the display?