Family Abduction Prevention Act of 2004 - Directs the Attorney General to make grants to States for projects involving: (1) the extradition of individuals suspected of committing a family abduction back to the State from which the child was taken; (2) investigation by law enforcement agencies of family abduction cases; (3) training for law enforcement agencies in responding to family abductions and recovering abducted children; (4) outreach and media campaigns to educate parents on the dangers of family abductions; and (5) notifying law enforcement authorities of the name and address of anyone requesting the school records of an abducted child. Requires that not less than 50 percent of the cost of a project for which a grant is made be provided by non-Federal sources.