A week ago, Alex Ferguson, deputy director of the Illinois Department of Law Enforcement, gave a speech to a statewide parent-teacher association. Afterward, a woman approached him. She was Janet Hicks. They knew of each other, but had never met.

Hicks' ex-husband had disappeared with their two daughters almost 7 1/2 years ago. Impelled by her own loss, Hicks founded an organization to help find missing children and worked with state officials like Ferguson.

Yesterday Ferguson recalled that Hicks had said to him, "You know, I've had such success in finding children, I don't know why I can't find mine." And even as he recounted their meeting, at that very moment, Janet Hicks was being reunited with her two daughters, whose photographs had been shown Monday night in NBC's documentary "Missing: Have You Seen This Person?"

"We understand," Ferguson said, "that the father told them their mother was dead."

There were no bells -- only flickering lights -- on the 40 telephones lined up in rows in the donated offices in Crystal Square III in Arlington, where volunteers and staff of the National Center for Missing and Exploited Children were poised Monday night to answer hot-line calls following the third NBC showing of "Adam."

And it was a good thing. A few seconds before 10, the lights flickered on all 40 phones almost simultaneously as the roll call of more than 50 missing children and the hot-line number (1-800-843-5678) appeared on TV screens following the award-winning docudrama about the disappearance and grisly death of 6-year-old Adam Walsh.

Volunteers, in shifts, worked through the night Monday and all day yesterday and will continue around the clock at least through Friday. By late yesterday afternoon there had been 3,522 calls, 1,050 from people who believed they had spotted one or more of the missing children whose photos were shown.

Most calls were from people wanting information.

"Missing" was beginning on a TV monitor in the phone-bank room, but only the phones demanded attention.

John and Reve Walsh, the real parents portrayed in "Adam" by Daniel J. Travanti and JoBeth Williams, came to lend support and to talk to troubled parents. Earlier they had been at the White House Rose Garden to hear President Reagan's resolution calling for private-public cooperation on the problem.

Linda Otto, who produced "Adam," and Joan Barnett, its executive producer, were there, too -- both at the White House and with the telephone volunteers until after midnight. "Adam," they say, was more than a movie.

"It changed all our lives," said Barnett. "You always make friends and loved ones on film sets, but on this one, we meant it."

In Kettering, Ohio, a suburb of Dayton, school officials were watching "Missing." They watched as pictures of Janet Hicks' daughters, Kathleen and Deborah Caruso, were shown -- not as they were more than seven years ago, little girls of 6 and 8, but as a medical illustrator calculated they would look today, as adolescents.

The Kettering officials recognized them. And they called the hot line to Crystal City. A volunteer wrote something like 'this looks like a good one' on one of the forms the volunteers kept by their phones. A specially trained law enforcement "technical assistant" evaluated the Kettering report and called Alex Ferguson, because the girls were declared missing in Illinois.

Ferguson, who said yesterday he felt as though he'd aged six years overnight, alerted the Kettering police, who had the girls' house under surveillance by 1 a.m.

John and Reve Walsh still mourn their son Adam, who was abducted from a Florida shopping mall in 1981, and they probably always will. Their agony was exacerbated by the discovery that the police were more willing to handle reports of a stolen car than of a stolen child. Eventually Adam was found, brutally murdered, but the Walshes became unswervingly committed to "making the country safe for these little people."

Since the tragedy, they have had two children -- Meghan, nearly 3, and Callahan, not quite 5 months. But as John Walsh puts it, "There is always one missing, the big brother they never knew . . ."

Repeated showings of "Adam," admits Reve Walsh, are "difficult," but each broadcast brings identifications and reunions -- "42," she says, "from the first two showings."

One thing that haunted Janet Hicks, she said Monday night on "Missing," was that the breast cancer she appears to have conquered might threaten her daughters, and that she might never be able to alert them.

Her plea to "neighbor, friend, teacher" was moving, and, as it turned out, productive.

After watching the house all night, the Kettering police watched the girls board a school bus. Only then, when the police were sure they would put them in no jeopardy, did they stop the bus, escort the girls to the station and, later, arrest the father.

At this point, Ferguson said, he put Hicks, along with a staff psychologist and two law enforcement agents, on a plane to Kettering.

Two members of the House of Representatives -- Tom Lewis (R-Fla.) and Edward F. Feighan (D-Ohio) -- joined the volunteers, as did Sen. Paula Hawkins (R-Fla.), who has been a leading voice for children's rights.

The phone bank and the computer data base were organized by National Center staffer Carla Branch, a social worker who has worked with Linda Otto on a series of public service spots on missing children that air on NBC-owned and operated stations, including Channel 4 here.

Branch, who is blind -- her golden retriever guide dog Tasha is only slightly discommoded by the hubbub -- knows the cases, say her colleagues, nearly as well as the newly updated computer. She designed the data base, she says, but her husband, a computer programmer at the Defense Department as well as a child center telephone volunteer, "is the real computer genius. I tell him what we need, and he does it."

Given enough information from parents -- dental records, medical scars, any kind of abnormality -- the computer can "sort all the information by any items . . . by blue eyes. So if we get an unknown child, we can search and see if we get a match."

One child, initially scheduled to be included in Monday night's roll call, was identified because a National Center technical adviser thought he recognized a type of clothing.

The center had been called by Texas officials to help identify "a young boy" who had been in the Dallas County morgue for three weeks. Jay Howell, the former Florida prosecutor who helped John Walsh in his initial, vain search and who now is executive director of the center, said the description of the boy's clothes sounded like that of those worn by a missing girl on the center's roster.

"Oh, no, the coroner already examined this child," said the Texas official. "It's a boy."

"Check the dental records," insisted the center staffer. And, said Howell, "the young boy who had been classifed as such after an autopsy was actually, in fact, the missing Texas girl."

John Walsh is furious over this incident. "Oh sure, we've come a long way," he said. "The movie 'Adam' did an incredible amount," but, he said, "we can spend 17 billion dollars on a space shuttle and we still can't tell the sex of a murdered child?"

By late afternoon yesterday, another child on the roll call had been found alive and well. Eight-year-old Melissa Klein, who disappeared from New York with her father a year ago, was identified on her way to school in California. An anonymous phone call to a California sheriff resulted in her father's arrest and an imminent reunion with her mother, who left New York for California within the hour, center officials said.

John Walsh has been working the states, the "50 feudal governments," and he is "still angry, still frustrated, still burning" with the need to make the system work for the little people. Among other things, he is trying to persuade states to institute background checks for schoolteachers.

"It's just so hard," he said. "In this country you cannot be a policeman or a lawyer or a doctor without a criminal record check. In 34 states you can't be a hairdresser. You can't work in a lottery, you can't be a groom, a lowly minimum-wage groom, but" -- he took a breath -- "you can be a teacher, a Big Brother, a Boy Scout leader, a day-care center worker or owner or operator, even if you're a previously convicted child molester or murderer. Where are our priorities?"

Abductions by parents also are of concern. "Police," says Joan Barnett, "mostly think it's no big deal if the child is abducted by the parent. But in lots of cases it is a big deal."

"We have to dispel that myth," says Linda Otto. "Parents do not kidnap children for the most part because they love them. They kidnap them because they want to get even with the other parent . . . There's only one victim there, and it isn't an adult."

There is, they all agree, a long way to go. But there is a lot of hope. And they all knew it even before the first airing of "Adam."

Barnett and Otto have been close friends for two decades, and tend to finish each other's sentences, especially telling this story:

"A picture of a 12-year-old girl, kidnaped a year before by her mother and her mother's boyfriend and taken halfway across the country, appeared in a TV Guide story about 'Adam.' The girl had been told by her mother that 'nobody wants you. You have to stay with us.' She never understood what happened, but then she saw a little blurb under her picture about how she was kidnaped, how her father and her grandparents were looking for her . . .

"She was the first one home."

Alex Ferguson was worried. It was getting late yesterday, and he hadn't heard from the people he sent to Ohio with Janet Hicks.

Then, finally, he was advised they were all on their way back -- with the girls.

"I'm not sure exactly what was going on," he said carefully, "but I think it's safe to say there were the appropriate emotional reactions."

"Crying?" he was asked.

"Crying," he said.

Wherever John Walsh goes, of course, parents of missing children beg for his support, his advice. He tells them, "You've got to be strong. When you're so tired you want to go under the bed and die, you've got to take that picture out one more time. Don't give up. It will try to wreck your marriage. You'll go broke . . . But you've got to keep going."