Political Candidate Personal Responsibility Act of 2004 - Amends the Federal Election Campaign Act of 1971 with respect to the publication and distribution of statements and solicitations to: (1) subject a printed communication that is transmitted through the Internet to the same requirements applicable to newspapers, magazines, and other print material; (2) require a campaign communication that is paid for and authorized by a candidate or a candidate's authorized political committee (or its agents), or that is paid for by other persons but authorized by a candidate or the candidate's authorized committee (or its agents) and makes any direct reference to another candidate for the same office, to contain a photo of the candidate and include a printed statement that the candidate has approved the communication; and (3) subject Internet and prerecorded telephone communications to applicable requirements with respect to communications by candidates or authorized persons that pertain to radio and television.