It was all running fine until I was looking at the sound options and clicked on the Sound Profile, which was blank. Then the analogue output just disappeared from the selectable outputs and now I have no sound.
I have tried flushing alsa followed by a reboot to no avail, if that is even relevant to my situation, as that was a common suggestion during my Google searches.
Well, either I'm interpreting these values wrong or the kernel doesn't even see an analogue ouput. You said that it was working fine before clicking something in the sound options. Can you confirm the card is working (e.g. under Windows). Did you do any recent updates?
I've had similar issues with pulseaudio before, and it generally causes a lot of headaches for me. Try reinstalling pulseaudio using these instructions: http://askubuntu.com/a/475665 . Works occasionally for me.
sudo apt-get install alsa-utils Reading package lists... Done Building dependency tree Reading state information... Done alsa-utils is already the newest version. alsa-utils set to manually installed. The following packages were automatically installed and are no longer required: linux-headers-generic-lts-utopic linux-image-generic-lts-utopic Use 'apt-get autoremove' to remove them. 0 to upgrade, 0 to newly install, 0 to remove and 0 not to upgrade.
Check if you can find the ~/.pulse/ and ~/.config/pulse/ directories and rename them (e.g. pulse-old) - you could also just delete them, however renaming them is the secure way.
I have had similar problems. In short, it's PulseAudio's fault and there are two simple ways to try to deal with it. The one I recommend trying first is
(sudo) apt-get install pavucontrol
...which will give you a slightly less stupid audio source/mixer control than the one that comes with Gnome by default, and will hopefully allow you access to your analog inputs and outputs from any user account.
If that doesn't work, uninstall everything related to PulseAudio, especially pulseaudio-module-x11 which, at startup, takes command of all audio sources and then fails to manage them intelligently, as you've discovered. The reason I recommend this only if the first approach fails is that pulseaudio is that other programs may depend on pulse. God only knows why so many developers have chosen to access the audio subsystem via pulse rather than ALSA, but they have.