Presidential Succession Act of 2004 - Removes members of Congress from the line of Presidential succession, such that the Secretary of State is the first in line in the event the President and Vice President are unable to serve. Adds the Secretary of Homeland Security to the line of succession immediately following the Attorney General. Provides that any officer serving as acting President serves either until a new President is elected or the disability of the President or Vice President is removed. Allows an individual to act as President without resigning from the Cabinet position which qualified the individual to act as President. Grants compensation for an acting President at the rate the President would receive. Provides that the line of succession remains the same if an acting President is unable to serve. Prohibits an officer from serving as acting President unless the officer is: (1) eligible for the office of President under the U.S. Constitution; (2) appointed to a Cabinet office, by and with the advice and consent of the Senate, prior to the time the powers and duties of the President devolve to such an officer; and (3) not under impeachment by the House of Representatives at the time the powers and duties of the office of President devolve to such an officer.