Peyton Valiente was gravely injured two years ago at an Ewa Beach day care, and no one was ever held accountable for the abuse.
The Valientes believe police did a poor job investigating the incident because the babysitter's husband is a former Honolulu police officer.
Chelsea Valiente, Peyton's mother, said she wants -- and deserves -- answers.
"Not only have closure, but justice for an innocent child that was so severely harmed," she said.
In early 2015, Peyton suffered severe head injuries in his babysitter's care. The unresponsive child was hospitalized with bleeding on his brain and eyes and finger-like bruises on his body.
No charges have been filed to date.
"It's completely frustrating," Valiente said. "Not just frustrating, but very disappointing. Especially to know that we could have had a different outcome to this date had the initial investigation been done properly."
The Valientes and their supporters want state Attorney General Doug Chin to step in and hopefully assemble a grand jury investigation.
"This is a case that hits super close to home regarding Hawaii's keiki," said state Sen. Will Espero. "We are asking the attorney general to pursue this case as far as he can."
The family said they were notified by HPD that files have been sent to the AG's office for consideration after city Prosecutor Keith Kaneshiro said his office would not take up the case.
In a letter, Kaneshiro said that "there was insufficient evidence to charge anyone with a crime" and that no new evidence has been presented.
He added that convening an investigative grand jury would not be productive if witnesses do not cooperate.
"We believe it is a serious dereliction of duty because the little boy was assaulted and the assailant has not been brought to justice," Espero said. "The assailant is still out there."
The state Attorney General's office has not commented on whether it plans to take the case. The Valientes have also filed a civil lawsuit against the babysitter and her family.