This probably has to do with how the audio is being output from the PS4. Go into your PS4s settings and set it to output only stereo audio. Chances are right now you have it outputting 5.1 PCM or Dolby/DTS bitstreamed audio, which the 3.5mm jack wouldn't be able to output.
That device also seems to have a 5.1/2.0 audio switch which looks to change between the coax and 3.5mm ports. Make sure that switch is set correctly too.
So to be clear you have a HDMI cable connected to your computer's VGA card and you have it going into a converter that changes it to a DVI and it has a audio cable coming out of it you have plugged into your monitor speakers?
You're not giving us enough information as to what is connected to where on the converter.
Long story short, HDMI and DVI use the same signal format for digital video, they are just wired differently, so they technically don't have to be "converted." DVI, however, does not output audio. You're device is likely meant to split an HDMI input into separate DVI and audio outputs, and maybe even work the other way around joinging DVI and audio inputs into a single HDMI output.
So, if you are connecting you're PCs video output via DVI and expecting to get audio output out of that DVI signal, that's not going to happen as DVI does not output audio.
Ok, heres the specics. I have an old rear projection tv with dvi input connected to the converter wich is connected via hdmi to my playstation 4. The video comes through, but the converter offers a coax audio out, and a 3.5 mm audio out for the audio signal from the hdmi. I have the 3.5 mm out connected to my stereo system, but nothing is coming through. Its a revesun hdmi to dvi converter. I have not tried to connect the audio via the coax cable input on the stereo system, bu I guess I might have to try that next.