Moriarty was kidnapped by Australian government agents (see: Australian Aboriginal and Torres Strait Islander Children) while at school. When his Aboriginal mother went to pick him up one day he had disappeared, along with other children. He was four years old. Although she sent his uncle and step-father to find him, they were unable to. They did not see one another until he was an adult.
He lived in a succession of children's homes and foster homes around Australia, sometimes physically abused, cold and hungry, but sometimes happy: "We were to become civilised and we were to be punished if we spoke the Aboriginal language." After leaving the care system he was apprenticed to a fitter and turner, played football (soccer) and was a civil servant, before opening the Balarinji Design Studio with his wife.
Moriarty is also a painter and holds the record for the largest portable art works in the world: the exteriors of two Qantas 747 jets, which he painted with Aboriginal motifs for the 2000 Olympic Games.