Weird Noise (Possible gas engine problem)

So my car seems to be a totally different car in the past few months after this last winter. It was extremely cold and snowy so I think that might have something to do with it.

The Car:
Car is 2008, 52k on it.

The Problem:
The gas engine engages at very weird times. There is the jerk and noise from the gas engine at almost all times. The acceleration feels like it is 25% of what it was before. Braking seems to be diminished too and I have to depress the brake fully for a second or two before the gas engine actually shuts off. In addition when the car was new, it would not engage the gas engine when you depress the accelerator in neutral. Now you can rev the enginer.

Oil has been recently changed but problem was even before oil and the oil change didnt' seem to affect it. Air filter was replaced.

Took it to Toyota and they said they didn't notice anything. It was a very warm day that day, 72. They only drove on freeway and probably didn't take the time to fully diagnose it.

The question:
Has anyone had this problem? Does anyone know what might be causing this?
Is it a CPU problem?

 

Can you elaborate please Bob? How would I solve the battery issue other then waiting for the weather to get warmer?

As for the N question, I was just curious one day to see what would happen in neutral.

 

Bob,

I did some digging and it does sound like my car does not fully go into stage 4. Probably because my commute is so short and the weather has been so cold is does not adequately warm up the ICE.