Would you believe I don't own that model?
No really

Wonder if it contains Sony's CXD1125, 1135 or CXD2500 chip inside?
The first two have the digital audio signal on pin 27. With CXD2500 you'd tap pin 60 to get it.

Seems likely D504 has one of those chips in; however, this site suggests it would probably be mounted on the under side of the motherboard.

I got lucky doing the mod on my CLD-S201, since the audio is on a daughter card (mounted vertically) giving easy access to both sides of the circuit board. It's a bottom-feeder in features and probably picture quality too, but I only use it for ripping. For that purpose, bit-accurate is good enough.

With basic soldering skills, adding S/PDIF can be fairly easy on some players.
If D504's your new one, what's the old?