Maybe you should read this forum a bit. Seems kernel 5.4 works for them.
If you want to try
sudo apt install linux-headers-5.4.0-91-generic linux-modules-5.4.0-91-generic linux-modules-extra-5.4.0-91-generic linux-image-5.4.0-91-generic
Reboot, enter grub and select the 5.4.0-91 kernel
gonna try that. But what does it mean "enter grub" ?
Ok got it.
I tried
i did what you said.
Still not working.
When you boot, you will see the grub menu where you can choose to boot ZorinOS or Windows.
Before grup times out.
Select Zorin Advanced Options.
Then choose 5.4.0-91-generic which should be listed if installation is done.
yes i found it, choosed it, and still no sound.
seem to be a pretty serious problem.
On the link that you sent me... its a bit chineese for me 
Go into alsamixer again and [F6] to select [HD-Audio]
Post screenshot of alsamixer after that.
No that is from the HDMI not HD-Audio.
Can you not select HD-Audio using [F6] now you have kernel 5.4.0-91 ??
I seem at a loss to help here.
I cannot understand why in "HD-Audio Generic" you have "ATI R6xx HDMI" and only S/PDIF's showing.
The websearches done here earlier for "ATI R6xx........" suggested a much later kernel (5.14, or 5.15) maybe required. But not a definitive answer, just says "Try installing".
Really dont know... do you think its worth asking the Zorin pro support ?
I think so in your case, but may take time for a reply. In your message to the dev's, include a link to this forum thread, as that will help to explain the problem and what has been looked at so far.
Maybe after the Christmas and New Year holiday's over maybe more users will be back here and some bright spark may think of a potential solution.
@Aravisian @Michel Got any more ideas.
ok thanks anyway guys
The problem is that his card get fixed in kernel 5.13 and up. Zorin uses 5.11.43
https://bbs.archlinux.org/viewtopic.php?pid=1982889#p1982889
@Rigge, can you download Pop! OS 21.10 and boot it live to see if the sound issue is gone ? Just for testing purpose because i know they use kernel 5.15.8
Hi Michel,
I tried.
Its exactly the same. Nothing works with Pop OS 21.10, still this "dummy output", i tried everything we tried here with Zorin.
Weird, i almost start thinking this is a hardware issue. The only thing i can think of is trying to play with the pin settings.
More details can be found in this topic.
Pulseaudio...
Wasn't sure if this was a nod to me!
Give yourself ownership of /etc
sudo chown [your user name] etc
then create a folder and call it 'pulse off' and drag the pulse folder into it.
Now add all the ALSA packages you can find in Synaptic Package Manager but not the ones for Jack or Pulse or OSS. Also install QAS Mixer, QAS Config plus one more whose name escapes me. Launch QAS Mixer and you should see your audio device at bottom of mixer window unchecked. Check it and you should hear a slight pop indicating you now have sound.