Ubuntu – Dumthe output using 82801JI (ICH10 Family) HD Audio Controller

My computer at work which runs 11.10 exclusively, has been very very quiet for a few weeks now. I am not sure when exactly the sound stop working but it was after the upgrade to oneiric since I remember listening to music just before the upgrade.
I tried many suggested solutions out there but it still does not want to work. Its not a case of sound being mute or lowered.

When I play music I can see activity in the pulse audio volume control (under the playback tab there is a progress bar that shows activity). But there is no sound coming out of either front or rear 3.5mm jacks or the HDMI (through monitor). I have Unity, Gnome3 and XFCE installed side by side and neither of them make a squawk!
Anyways, I really like to know how to debug and fix this issue. I am comfortable using the terminal, and if you guide me I can provide debug info. What can I do to find out what the issue is and to fix it?

Sound is onboard:
00:1b.0 Audio device: Intel Corporation 82801JI (ICH10 Family) HD Audio Controller
03:00.1 Audio device: nVidia Corporation High Definition Audio Controller (rev a1)

Update 1: As pointed out by fossfreedom in the comment, the issue seems to be in the device for sound output. Somehow my real devices have been replaced with a "dummy device". How can I add my on-board sound device to this list?

Update 2: I tried running sudo alsa force-reload as suggested and here is the error I get:

sudo alsa force-reload 
Unloading ALSA sound driver modules: snd-intel8x0 snd-ac97-codec snd-hdacodec-hdmi
snd-hda-codec-realtek snd-hda-intel snd-hda-codec snd-hwdep snd-pcm snd-seq-midi 
snd-rawmidi snd-seq-midi-event snd-seq snd-timer snd-seq-device snd-page-alloc 
(failed: modules still loaded: snd-hda-codec-hdmi snd-hda-codec-realtek
snd-hda-intel snd-hda-codec snd-hwdep snd-pcm snd-timer snd-page-alloc).
Loading ALSA sound driver modules: snd-intel8x0 snd-ac97-codec snd-hda-codec-hdmi
snd-hda-codec-realtek snd-hda-intel snd-hda-codec snd-hwdep snd-pcm snd-seq-midi
snd-rawmidi snd-seq-midi-event snd-seq snd-timer snd-seq-device snd-page-alloc.

Update 3: Here is the detailed list of my sound devices as requested:

sudo lshw -class multimedia
*-multimedia            
   description: Audio device
   product: High Definition Audio Controller
   vendor: nVidia Corporation
   physical id: 0.1
   bus info: pci@0000:03:00.1
   version: a1
   width: 32 bits
   clock: 33MHz
   capabilities: pm msi pciexpress bus_master cap_list
   configuration: driver=HDA Intel latency=0
   resources: irq:17 memory:fbefc000-fbefffff
*-multimedia
   description: Audio device
   product: 82801JI (ICH10 Family) HD Audio Controller
   vendor: Intel Corporation
   physical id: 1b
   bus info: pci@0000:00:1b.0
   version: 00
   width: 64 bits
   clock: 33MHz
   capabilities: pm msi pciexpress bus_master cap_list
   configuration: driver=HDA Intel latency=0
   resources: irq:56 memory:f9cf4000-f9cf7fff

Update 4: This is getting interesting. I thought I found the solution when I saw that my user did not have permission to use the sound device.

So I add myself to the audio and video groups and rebooted. Now the sound devices are available under choose a device for sound output.

With lots of hope I selected Internal Audio Analog Stereo as the device, but still no sound at all is coming out of the system :(. I tried using the speaker test tool as well as playing music while trying out all the different jacks. I also tried switching between HDMI and the Internal Audio, still no luck. What else can I do next?