I had a DTT3500 once. Sold to a friend who fried it... Loved the collection of bezel provided with it 🤣
The sound was good. The pinout should be compatible. I don't know why Cambridge SoundWorks would use the same connector with different wiring for hardware of the same period.
But it is possible that the FPS2000 cable is not fully wired. Cost reduction maybe. You should try to test continuity on the pins to see that.
If I remember correctly, I connected it through my SB Live! 5.1 Platinum using the same DIN connector accesible from a slot bracket connected to the sound card internal deck (black cable with green mini-DIN on each side). But I also remember having a cable with the mini-DIN plug from one end and the classical green, black, orange, grey jacks. That would mean analogue audio. Need to check that, I probably have photos.
If your cable is not fully wired, that's a shame because such cables, sure are impossible to find...

Just checked my photos.
I fact, it was a 15 cm adapter Digital DIN to an orange jack with 4 sections to plug in the digital output of compatible Creative Labs sound card and not green, black, orange and gray as I remembered. That makes more sense!

Datadrainer wrote on 2021-09-29, 15:21:

Just checked my photos.
I fact, it was a 15 cm adapter Digital DIN to an orange jack with 4 sections to plug in the digital output of compatible Creative Labs sound card and not green, black, orange and gray as I remembered. That makes more sense!

Are you able to share the photo? I am curious if my cable looks the same.

Nope, sorry. That's shots of the room and the PC at the time. There is no detail and I don't want to share my photos.
But where I can help you is with some info. From what I have found the adapter allows transmission of 3 stereo (uncompressed) S/PDIF signals {(FL,FR),(RL,RR),(C,SW)}
Here are the plugs pinout:

As the original cable can transmit 4 S/PDIF stereo channels, maybe it was originally designed to support 7.1 audio systems. So if you have the sub-woofer producing bass, you should also have the center speaker to produce sound. If not, maybe there is a problem with your DTT3500 or maybe it's a software problem.
Hope this will help.