What causes the engine to go into a neutral mode, & lose power to the headlights

What is your question?

2006 Infiniti M35X with 114,000 miles My first observation of this problem that I'm about to explain was after I was hit in the back end while I was stopped. After being hit, I had no throttle. Upon turning the engine off and restarting the engine, I was able to access power by pressing the gas pedal. It ran fine for two months after that incident. My second encounter occurred as I was driving the engine went into a mode that was similar to me putting the car into neutral, but there was no power at the gas pedal. I found that by turning the engine off, waiting two minutes, I would be able to restart the car and there would be power by pressing on the gas pedal. In addition, I found that if I removed both of the cables from the battery, waited a few minutes, reattached them, I could start the car, and it would have power again. An incident while driving during nighttime was identical to each previous incident, but this time the dashboard and headlights went completely out and it was like I turned off my headlights and placed the car in neutral. I was able to move to the side of the road, turn the engine off, wait a few minutes, restart the car, and drive home without incident. This idling stage occurs each time I encounter this problem. The code was 2101. I replaced the throttle motor. This did not alleviate the problem. December of 2014 my vehicle was recalled by Nissan because of an issue (2006 M35) Infiniti had with the accelerator sensor. Nissan replaced the sensor. I thought that would surely be the fix and would correct the problem. Soon thereafter, the problem was repeated again. Do you have any idea(s) what may be creating the problem in my 2006 Infiniti M35X? Thanks in advance for any help you may be able to give me. Thank you, John