Junk Fax Prevention Act of 2004 - Amends the Communications Act of 1934 to prohibit a person from using any telephone facsimile (fax) machine, computer, or other device to send, to another fax machine, an unsolicited advertisement to a person who has requested that such sender not send such advertisements, or to any other person unless: (1) the sender has an established business relationship with the person; and (2) the advertisement contains a conspicuous notice on its first page that the recipient may request not to be sent any further unsolicited advertisements, and includes a domestic telephone and fax number (neither of which can be a pay-per-call number) for sending such a request.

Requires the Federal Communications Commission (FCC) to provide by rule that a request not to send unsolicited advertisements complies with legal requirements if: (1) the request identifies the recipient fax number to which the request relates; (2) the request is made to the telephone or fax number of the sender; and (3) the person making the request has not subsequently provided express invitation or permission to have such advertisements sent. Authorizes the FCC to allow professional tax-exempt trade associations to send unsolicited advertisements to their members in furtherance of association purposes.

Requires the: (1) FCC to report annually to Congress on the enforcement of the above requirements; and (2) Comptroller General to study, and report to specified congressional committees on, complaints received by the FCC concerning unsolicited advertisements sent to fax machines.