NEW YORK (CNN) -- It is one of the most notorious cold cases in recent memory. A 6-year-old girl, a child of beauty and privilege, was found dead in the basement of her home in Boulder, Colorado, on the day after Christmas 1996.



The strangulation of JonBenet Ramsey is also among the coldest of cases. Twelve years have passed, and again it is Christmastime, the season of JonBenet's death.



The investigation has taken many heartbreaking twists and turns, including a false confession and baseless suspicions cast for a time on the child's parents. After years of false starts, there are no solid leads.



For many, the images of this tragic story are indelible: A doll-like child smiling flirtatiously at the camera in flamboyant costumes, heavy makeup and grown-up hairstyles parading on a beauty pageant stage. A tiny, lifeless body, dressed in long johns, found on the basement floor by her father.   Watch how this case touched nearly everyone »



Just this past July, John and Patsy Ramsey were exonerated by police of having any role in their daughter's death. Patsy Ramsey died of cancer in June 2006.



FBI lab results confirmed that a man, yet to be identified, touched JonBenet's long underwear. This so-called touch DNA also was found in JonBenet's underpants, mixed with the child's blood.



Police believe the DNA belongs to the killer. They just don't know who he is. They are waiting for a match.



From the beginning, police focused their attention on Patsy Ramsey, placing the entire family under what authorities later would admit was a cloud of suspicion.



The investigators' working theory was that JonBenet's mother may have struck her in anger as punishment for bed-wetting, causing the little girl's death on Christmas night. Investigators theorized that a strangulation was then staged to direct suspicion toward an intruder or sexual predator.



Patsy Ramsey told police she awoke early December 26 and found a two-page, handwritten ransom note on a back staircase. It said JonBenet had been kidnapped by a "small foreign faction" and that she'd be executed if the Ramseys did not pay a $118,000 ransom.



The Ramseys checked JonBenet's room, discovered she was missing and immediately called 911.



When police arrived, they suggested that John Ramsey and a family friend, Fleet White, search the house. Shortly afterward, Ramsey and White found JonBenet's body in a wine cellar in the basement. The child's body was wrapped in a blanket, with duct tape across her mouth and white cord wrapped around her neck and wrists.



An autopsy showed the child had eaten pineapple shortly before she died. She'd been sexually assaulted, strangled by the cord and struck on the head.



Crime scene photos show two small burn-type injuries on JonBenet's head. Private investigators Ollie Gray and John San Augustin, working as consultants on the case, said the burns are consistent with marks made with a "stun gun."



Investigators also concluded that the paper the ransom note was written on came from a notepad in the Ramsey home, as did the broken paintbrush handle used to form the garrote.



However, the sources for the cord and duct tape were not found anywhere in the home.



Other nagging clues include an open basement window near where the child's body was found. A suitcase stood directly below the window, and appeared to have been used as a step. There was a scuff mark on the wall beneath the window. A footprint of a Hi-Tec hiking boot was found in the dust in the wine cellar and cannot be connected to anyone in the Ramsey family or their friends.



Police say they were initially suspicious of the Ramseys because there were no footprints in the snow outside the house.



Lou Smits, a lead police investigator on the case, resigned because, he said, the investigation "was misdirected and had developed tunnel vision, only focusing on the Ramseys as suspects and not following alternative leads."



The contradictory facts have caused problems in the case
What new technology cleared the family? Which family is under suspicion? Where did the crime take place? Who did the new touch DNA test clear? How many years were the Ramsey's suspected of the murder? When did the crime occur?
touch DNA Ramsey, basement of her home in Boulder, Colorado, on the day after Christmas 1996. John and Patsy Ramsey Twelve the day after Christmas 1996.
question: What new technology cleared the family?, answer: touch DNA | question: Which family is under suspicion?, answer: Ramsey, | question: Where did the crime take place?, answer: basement of her home in Boulder, Colorado, on the day after Christmas 1996. | question: Who did the new touch DNA test clear?, answer: John and Patsy Ramsey | question: How many years were the Ramsey's suspected of the murder?, answer: Twelve | question: When did the crime occur?, answer: the day after Christmas 1996.