Parnell, 76, died at the California Medical Facility in Vacaville on Monday, corrections officials said Tuesday.
He was convicted of kidnapping 7-year-old Steven Stayner in 1972 and keeping him until 1980. That's when Parnell abducted a second boy and Stayner fled, taking the boy with him.
Stayner's story was told in the television movie "I Know My First Name is Steven." He died in a motorcycle accident in 1989.
Stayner's brother, Cary, is awaiting execution for killing four women in Yosemite National Park in 1999.
Parnell was paroled after serving prison time for the earlier kidnappings. In 2004, he was sentenced to 25 years to life after he attempted to abduct another child.
Prosecutors said he asked the sister of his former caretaker to deliver a 4-year-old boy to his Berkeley apartment in exchange for $500. The woman went to police instead.