I installed a Gentex auto dimming rearview mirror with compass in my 2006. The instructions with the mirror indicated what each wire did. Obviously your mirror did not come with such instructions. The 2004 mirror was designed to attach to a plug in the overheat light region. (This can be accessed by GENTLY prying or using a trim stick.) I doubt that the plug is still there, but it might be, in which case just plug it in after threading the wire up behind the overhead trim by the windshield. If there is no plug, you can probably splice the wires. They are likely color coded to match the wires to the overhead light.
BR/YL dome lamp switch output
BR ground
BL/BR dome lamp control
RD/DG fused +
BR=brown, YL=yellow, BL=blue, RD=red, DG=dark green