Delaney grew up in Roxborough and has four brothers: Ed, John, Keith, and Patrick. While she was attending J. W. Hallahan Catholic Girls High School, she worked as a model for the Elite agency. Delaney first became known for her stint as innocent teenager Jenny Gardner Nelson on the soap opera All My Children, which also was her first job. in 1987 she also appeared as Jessie in Christmas Comes to Willow Creek. A 1996 profile article in Entertainment Weekly, on the occasion of her landing a prestigious television role at the end of this period, noted: “Delaney’s résumé is spotted with ridiculous roles that range from a nun in the Chuck Norris action movie, The Delta Force, to a possessed nymphomaniac in the soft-core horror film, Temptress. ‘There’s a lot of things I did to pay the mortgage,’ Delaney says resignedly.” Roles from this period include her 1992 appearance as Lucky Santangelo in the television miniseries, Lady Boss. Her first marriage to actor Charles Grant lasted from 1984 to 1988.
