Welcome to LQ!
Here's the ALSA
information about your soundcard. Is this your module?
It is incorrect to say that the module (driver for the soundchip) works
as root and doesn't work as user. Do not run your system as root; setup
and run as a normal user.
After a clean install of Slackware, open a terminal and as root issue
"alsamixer" and unmute with the M key, then turn up the sliders with the
up arrow key. Then press Esc to close the mixer, then issue "alsactl store"
to save the settings.
I can't believe you started out your tenure on LQ by double-posting