Melanie Grimsley, from Erne Park, Kesh, Co Fermanagh, and her older sister Amanda were left in the family's Austin Maestro while their mother went into a supermarket in Enniskillen.
Minutes later Pamela Grimsley ran out to find the car in flames. Amanda, whose third birthday would have been eight days later, was killed.
Melanie, who was pulled from the blazing car, suffered extensive burns to her face, head, hands and arms. She has since undergone numerous operations.
Mervyn Morrow QC, for the child, said the damages should take into account the fact that Melanie had been effectively deprived of the prospect of employment.
Her claim, brought by an uncle on her behalf, was against her mother, as the car driver, her father William, the car's owner, and two garages, Erne Engineering Company and T P Topping Ltd.
Insurance companies representing all the defendants have denied liability.
Mr Morrow said the fire authorities could not find the cause of the fire but said it was started by the courtesy light. It went on and off for no apparent reason, consistent with a loose connection creating a 'hot spot', he said.
Mr Morrow said attention had been drawn to 'this obvious inherent danger' but it had never been put right.
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