John and Samantha Allen, both 23, entered not guilty pleas to first-degree murder, conspiracy and multiple counts of felony child abuse in Maricopa County Superior Court stemming from the girl's death last month.
But investigators say family members fabricated the story to cover their actions, and that the girl had been locked in the box to discipline her for stealing a Popsicle.
They said she had been physically abused by family members for at least a year.
Investigators said Samantha Allen, the girl's cousin, watched as her husband John locked the girl inside the box, and both then fell asleep.
The Allens remain custody in lieu of a $1 million cash bond.
The girl's grandmother, Judith Deal, 72, and Cynthia Stoltzmann, 44, her aunt and legal guardian, also pleaded not guilty to multiple counts of felony child abuse in the case.
Police said Deal and Stoltzmann were not present during the incident.
They are in jail on a $500,000 cash bond.
"This child died at the hands of those who were supposed to love and care for her," said Sergeant Trent Crump, a spokesman for the Phoenix police. "This case has turned the stomachs of some of most seasoned detectives."
Crump said that when Ame was first caught, the Allens forced her to perform exercises, such as jumping jacks, running in circles and back bends, for over an hour.
They then ordered her to climb in the storage chest before locking it with a padlock.
She was found dead the next morning, apparently having suffocated.
Police said the child was 4 feet, 2 inches tall and weighed just 59 pounds.
The box she was locked in was less than 3 feet long, 14 inches wide and about a foot deep.
The girl was very dirty and wearing soiled clothes when found, with marks on her right knee apparently from "forceful contact with the interior lid," investigators reported.
Crump said she routinely slept in the shower with no pillow or cover after having wet her bed.
Crump said detectives were still investigating how the child ended up in the custody of her aunt but said she was one of over a dozen children who were living in that home and another with various family members.