The morning after her 15-year-old son was shot and killed by a mysterious motorist in Northwest Washington, a trembling Barbara Seaton struggled through one interview after another at her suburban Maryland home yesterday, hoping the publicity would help solve the Thanksgiving Day slaying that so far has left police and family members dumbfounded.

"It didn't make any sense. He had no enemies at all . . . He was just a typical kid," she said softly of her son, David, whom she described as a playful, music-loving teen-ager. Down the hall from the living room, where television cameras ground away, David's bedroom remained as he had left it on the last morning of his life: the walls decorated with autographed photos of Redskins, posters of Cheryl Ladd and Lynda Carter, roller skates and athletic socks on the floor and a fish tank in the corner.

Meanwhile, at D.C. police headquarters downtown, homicide Sgt. Robert Sharkey, the lead investigator into David's death, sorted through automobile registrations and anonymous tips, trying to figure out why an apparent stranger shot Seaton as he waited in a pickup truck at a stoplight.

"We don't get many like this; it's mind-boggling," said Sharkey, a 12-year-veteran of the homicide squad. The case so far lacks any motive, he said. "We keep going back to square one, trying to figure it out."

What police know is that an unidentified motorist shot Seaton in the head shortly after 9 a.m. Thursday as the pickup truck in which the youth was riding stopped at a light at First Street and Michigan Avenue, an intersection flanked by the parking lots of Children's Hospital on the north and the open fields surrounding McMillan Reservoir on the south.

The gunman, going west on Michigan Avenue, pulled alongside the truck and without warning fired a shot through a closed window of the truck's passenger side. The bullet struck Seaton in the right temple, knocking him into the lap of the driver, his friend, Ernie Rich, 19. The two had been headed to a Northwest construction site to finish some work before returning home for Thanksgiving dinner.

At the sound of gunfire, Rich said he looked to the assailant and saw a gun aimed at his own head, according to Mrs. Seaton and other family members. "He scooted down into the seat and then drove straight into Children's Hospital," she said.

Young Seaton was brought unconscious into the emergency room and died 30 minutes later. Sharkey said the brain damage was so extensive that he was, for all practical purposes, killed instantly.

After shooting Seaton, the gunman drove away at a normal speed down Michigan Avenue.

Based on descriptions provided by Rich and a motorist near the scene, a composite drawing of the gunman was released last night by police, who described him a thin-faced black man in his 40s with a medium complexion, who wore a moustache.

The gunman was also described as well-dressed and driving a white car with a black vinyl top and D.C. license plates. Sharkey said late yesterday that police are "almost positive" that the car was a Buick Skylark, Le Sabre or Electra 225, built between 1968 and 1974. Sharkey said police initially determined that there were 10,977 Buicks of all models with D.C. tags that were built between 1965 and 1980, and they are working with computers to narrow the list.

Sharkey said police have found that Seaton and Rich had no criminal record. Police have also determined that drugs apparently did not play a role in the slaying -- always a possibility during initially inexplicable killings.

Seaton and Rich were on their way to Holmead Place NW, where Seaton's stepfater, Richard Roberts, had been supervising a housing rehabilitation project for his firm, Cumbari Associates. Rich is one of Roberts' employes, and Seaton was helping out to earn some extra money. Seaton also held a part-time job as a Washington Post paper carrier.

Yesterday, Rich's red 1963 Chevrolet pickup truck, the passenger window shot out, was still parked in the Children's Hospital lot. "I don't think Ernie will ever drive it again," Barbara Seaton said.

Ernie Rich and her son were like brothers, Barbar Seaton said. Rich had moved in with Roberts and Barbara Seaton earlier this year.

Partly because he liked Ernie so much, family members said, David also moved in with his mother and Roberts last week after living for eight years with his father, Charles Seaton, Laurel accountant.

The move was one of several apparent coincidences that combined to put David in the killer's path Thursday. If the youth had stayed another week at his father's he might have been miles away from the slaying scene on Thanksgiving morning.

"His moving was a personal thing," Charles Seaton recalled yesterday."His mother and I felt he needed a change. He thinks an awful lot of [Roberts] and he really liked [Ernie]. He just wanted to be with them some, too. He wanted to do it and we went along with it, unfortunately."

David Seaton was known to his parents, his sister and his friends as a fun-loving boy whose favorite hobbies were music, rollerskating and sports, and who was just beginning to find himself.

He played electric guitar in a Laurel rock group called "Premonition," made up of several friends he had met while living with his father. His favorite song was "Stairway to Heaven," his sister Vicki recalled.

Just last week, David had picked out a new electric guitar that his father was going to give him as a Christmas present. "David was just starting to be a really good guitarist," said Phillip Ammon, 17, a member of the combo, which broke up earlier this year, but planned a renaissance. "He had a really good life ahead of him."

Seaton, described as bright but not a serious student, was off to a good start at DuVal High School in Lanham, where he transferred last week after moving to his mother's home in Seabrook. He scored 96 on an algrebra exam, the only test he had taken at DuVal. "I think maybe the change of schools gave him a renewed interest," Charles Seaton said of his son.

The youth's yearbook from Eisenhower Junior High School in Laurel was filled with playful salutations from classmates like: "David: to a cool, ugly fool who was in my science class," and "To a cool dude half the time, the other half a real jerk. Don't forget our fabulous softball team. See you at the skating rink."

David's move to his mother's house was apparently going well, Sandy Hill, a neighbor and friend, said. On the last night of his life, David and his stepfather went out together to buy a Thanksgiving turkey.

"They had such a good night together. They had a good week here," Hill said. "I'm just glad they got to have him at least for a week.