as root:
chmod 666 /dev/dsp /dev/mixer
This might work. I'm not so sure though, I think that Slack 9 actually has those set correctly from the get go...
Also, as root, you might try running
lsmod
to see if the correct kernel module is being loaded. You might also check /etc/rc.d/rc.modules to see if you can find the module for your sound device there. If so, try uncommenting it. Also, if none of that works, try changing the permissions on /etc/rc.d/rc.hotplug like
chmod a-x /etc/rc.d/rc.hotplug
as root.
Other than that, beats me.