The remains were discovered in 2012 on the island of Kauai. Steve Baugh told The SandPaper, a weekly in New Jersey's Ocean County, his family was told in late August they had been positively identified as those of Nancy Ellen Baugh.
The identification was done with help from the military laboratory that handles the remains of U.S. service members found in Vietnam.
Baugh, who grew up in Beach Haven, N.J., was 20 when she disappeared. She and her boyfriend, Paul Featherman, 27, had moved to Hawaii and were working at the Hanalei Bay Resort.
In June 1979, Featherman was shot and killed in the home he and Baugh shared. She disappeared.
Neighbors later reported hearing screaming and a gunshot but apparently were afraid to call police at the time.
Steve Baugh told the SandPaper in a story published last week he has heard a lot over the years from Hawaii residents about the case. He and his family were told of a group of brothers on Kauai who were apparently committing violent crimes in the 1970s with impunity.
He believes Featherman was shot when he tried to stop intruders from kidnapping Nancy.
Prosecutors in Hawaii told him the investigation is being reopened and that it will be treated like it is a "brand-new homicide," Steve Baugh said.
Over the years, the family, who had lived on Long Beach Island in New Jersey for generations, has thinned. Nancy's father and one of her three brothers have died, although her mother, Betty, 85, is still alive.
"Now we can have as much of a closure as we're ever going to get," Steve Baugh said. "I tell people that it's like 75 percent closure. When you never know, all of the questions are still there, and any one of those could be real, of what could have happened to her. This way, at least we know, and from what they can tell, they don't think she was alive long after she was abducted -- she was not held alive for years and tortured or abused. So a lot of good things come out of finding her remains."