Problems with no check engine light. Help!!

My 2007 prius has given me 5 years of perfect driving. Now at 160k miles it is giving numerous problems with absolutely no check engine lights. Or warning lights of any kind. Even the mechanics at a reputable shop whom specializes in prius are stumped.

My problems..... In order of occurrence..
The car at start up is at 1 bar of battery, instead of turning the engine on to charge it, the car only turns the engine on when the throttle is pressed, then immediately shuts off, the battery would not go higher than 2 bars the entire drive due to not being charged properly.

At a dead stop, the energy monitor shows the engine on, and powering the wheels, and battery.

Engine idle is very low, with a slight vibration, battery is at 5 bars yet the engine will not turn off, rather it shows that the car is charging the battery.

Last but certainly not least...
The car was driving fine, then from a stop light on, you press on the peddle, even to the floor, yet the car is completely unresponsive, then after approximately 5 seconds, the car gives a hard kick, accelerates a little, unresponsive, kick, then a very rough acceleration up to cruising speed.
This problem is randomly occurring now, at times the car drives fine, except for previous odd behavior, then without notice or pattern. This again.

This website is my last option. Seeing that as I said I have no lights, and even the mechanics being stumped.
Please, please, please. Any advice helps!

 

I will take it in today, thank you for the advice!!! Very much appreciated.

 

It still has the original. While taking into Toyota it gave a new symptom. It did notnot want to stay in drive. At a stop it would consistently shift itself out of drive or reverse and into neutral. After approx 5 tries it would stay in drive until you stop again.

 

The only thing I have replaced is the 12v. Which I checked and is fine. And the engine water pump.