pulseaudio not working : "Home directory not accessible: Permission denied"

Ok, I got it in the end.

It was a permission problem with my home folder and pulseaudio.

Run the following command to fix the $HOME directory permissions for the current $USER:

sudo chown -R $USER:$USER $HOME/

I used http://www.linuxquestions.org/questions/linux-software-2/problem-with-pulse-audio-834041/ and http://ubuntuforums.org/showthread.php?p=6208727 as sources.

The solution for me was to fix the permissions using the following command: sudo chown -R lionel:lionel /home/lionel and then using pavucontrol to unmute the output.

The gnome indicator is still greyed but music is back, and that's a good thing.

(I'm only trying to improve the marked answer slightly, but with a little bit more than I think works in a simple comment. I thought it useful at least to post for the next guy. If a moderator disagrees this answer could be demoted to a comment on the selected answer if more appropriate.)

The reference to pavucontrol was rather cryptic and this response somewhat less usable to me, but it did put me onto a solution.

I had none of the permission and ownership problems that seem to be the main focus here. pavucontrol, which I had to install for just this purpose, did allow me, on the playback tab, to change from "High Definition Audio Controller Digital Stereo (HDMI)" to "Built-in Audio Analog Stereo" and my audio began working again as it had before.

I still don't know I got my ThinkPad (running Mint 13 which is basically Ubuntu 12.04 LTS) into this unworking state, but this is how I was able to get audio (in particular, Audacious Player using Pulse) working. I hope this helps.