Newborn Screening Saves Lives Act of 2004 - Amends the Public Health Service Act to require the Secretary of Health and Human Services, acting through the Associate Administrator of the Maternal and Child Health Bureau of the Health Resources and Services Administration, to awards grants to eligible entities to: (1) provide education and training in newborn screening and congenital, genetic, and metabolic disorders to health care professionals and State health department laboratory personnel; (2) develop educational programs about newborn screening for parents, families, and parents advocacy and support groups; and (3) establish, maintain, and operate a system to assess and coordinate treatment relating to congenital, genetic, and metabolic disorders.