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
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
Other than that, beats me.