What do the "F+" and "F-" pins on a power supply unit stand for?
My guess is that the media player used a vacuum fluorescent display (VFD) and that the -24 V was required for that.



Figure 1. Vacuum fluorescent display. Source Wikipedia commons.



+5 V is clearly for the logic.



VFD filaments



Figure 2. VFD cross-section showing filaments. Source: Noritake Electric.

Thanks to @DaveTweed for suggesting "filament" for F+ and F-. This led me to the Noritake Itron page linked above. They state:


  The electrons emitted from the cathode filaments are controlled by the grids. When the grid is supplied with a positive voltage, it attracts the negative electrons, diffuses them and, due to their acceleration, many flow through the grid mesh towards the anode (opposite charges attract). However, when the grid is supplied with a negative voltage, it repels the negative electrons and prevents them from reaching the anode (similar charges repel). 


The rest of the article is quite interesting and detailed. I was not aware of the details of operation. I think the filaments are visible as seven light horizontal lines in the photo of Figure 1.