Alsa was installed as per usual:
alsa-base, alsa-utils, alsa-tools, libsound, alsamixer, (and dependencies) and lastly volumeicon (started from Openbox autostart file).
alsactl initdid the trick and everything seemed dandy.
Unfortunately, the sound worked alright only to first reboot. Then it didn't anymore, and volumeicon also disappeared (and refused to start from terminal with quite a lengthy fail-message).
I tried various stuff to diagnose and fix:
alsactl initagain, and heavier
Pried from terminal with:
lspci | grep audio
and even with hwinfo (install from repo)...
Visited alsas' home for information and for possible source download.
Peeked into files:
1. Nvidia or no, the drivers are:
snd-hda-intel=> card0 (default), and not working for me,
snd-intel8x0=> card1, and working when manually chosen.
2. Solution is that the second one should be the first, default choice. And then there wouldn't be also need to change the last block in volumeicon file:
sudo nano /etc/modprobe.d/alsa-base.conf
After lines of 'install' and before 'options' I added two lines:
options snd-intel8x0 index=0
options snd-hda-intel index=1
sudo alsa force-reload
And there was sound! And it still is - also after reboot.