Leaving the victim's 3-year-old daughter alone with her dying mother, Parker then drove with the baby in her lap when a state trooper stopped the car and sent the child to a hospital in nearby Idabel, Oklahoma, authorities say. The child later died.
Witnesses said Parker, who could not conceive after a hysterectomy, had offered $100,000 for a surrogate mother and told her boyfriend that she would have an induced delivery the day of the killing.
Defence attorney Jeff Harrelson asked the six male and six female jurors not to fall prey to their emotions and to keep an open mind.
"It's a complicated case, factually and emotionally," he said. "The law is the lens and filter you must view these facts through. Sometimes it's not black and white but a shade of grey."
Parker could get the death penalty or life in prison without parole if convicted of capital murder. Attorneys estimated they would present at least two weeks of testimony.
New Boston is about 30 kilometres west of Texarkana, Texas.
- AP