WE'VE TRIED EVERYTHING," SAYS New York City police detective Jerry Giorgio. "We've had national publicity. We've used the FBI, and psychologists and anthropologists and psychics. But now it's time to put our baby to bed."

On Friday, July 23, the detectives of Manhattan's 34th Precinct finally buried Baby Hope, the murdered child unidentified for two years, who had become, says Giorgio, "like one of our own." In St. Elizabeth's Church, in the precinct's northern Manhattan neighborhood, nearly 1,000 mourners joined the detectives to offer a funeral Mass and bid the child a tearful goodbye.

The body of the 4- or 5-year-old girl had been found on July 23, 1991, bound with rope and stuffed in a picnic cooler just off the Henry Hudson Parkway. She had been starved, sexually abused and, finally, suffocated. Her remains were kept in the morgue in the hope that her family would be found. That forlorn hope inspired the name the detectives gave her.

"Who was she? Where did she come from?" asked a still bewildered Lt. Joseph Reznick in his eulogy. "And how could anyone do this to a little girl?"

Sustained by such questions, as well as by their own anger, the detectives logged thousands of hours chasing down tips. Many of them kept a computer-generated sketch of the child, along with photos of their own kids, over their desks.

Detective Giorgio's wife, Catherine, bought the white, size-4 dress that Baby Hope was buried in. The 40-person squad chipped in for the $1,000 headstone and other funeral costs.

Even now the case remains open. Detectives hope news of the burial may lead to the call that will finally bring them the killer. But relief was clearly the dominant emotion at St. Raymond's Cemetery in the Bronx. "We are the only family she has," said Giorgio. "Now she is at rest, and we can come and visit her."