Brogan Fenton was pronounced dead within 40 minutes of the incident at the family home on Lingwell Nook Lane in Lofthouse, Wakefield.
The hearing was told that around 2.10pm on Wednesday, January 4, the boy’s mum went to her car, which was parked in a double garage at the bottom of their driveway.
She activated the electric roller shutter door using her key, then got into the vehicle, which was facing out of the garage, intending to collect her older son, five, from school.
The inquest was told that she was unaware Brogan was nearby and as she moved the car out of the garage, she made contact with the boy and he became trapped.
Coroner David Hinchliff said: “Realising that an incident had happened in respect of Brogan, his mother ran into the house to get immediate help from his grandfather.”
Brogan’s grandad rushed to the car to free the youngster.
Paramedics and the Yorkshire Air Ambulance were called to the scene.
But an air ambulance doctor confirmed Brogan’s death at 2.47pm, the inquest was told.
Mr Hinchliff said an interim post-mortem report gave the cause of his death as a head injury.
He adjourned the inquest pending the outcome of further enquiries.