As a primary test, for example, try the following on a terminal:
% amixer -c1 set "Auto-Mute Mode" "Enabled" % aplay -Dplughw:1 -vv some-your-file.wav
where some-your-file.wav is any WAV file you'd like to hear.
If you're using PulseAudio, try like below instead:
% pasuspender -- aplay -D plughw:1 -vv some-your-file.wav
Does it play anything? Try both the headphone plugged and unplugged.
My apologies, I did seriously try to figure out how to figure this out and didn't come across anything that made any sense. So, I thought it was a kernel bug...
Your suggestion to try aplay did indeed produce sound. It is the first sound I was able to get out of this configuration ever. I attached the output of alsa-info.sh with aplay playing, and with mplayer playing and not working, and the diff. Thanks for your help, at least now I have some clue about where to look.