had the same problem on my 10.10 install. I fixed it by clicking on the volume icon on the right side of the top panel>sound settings. If 12.04 uses the same sound settings as 10.10, you should now see a window with an output volume slider on the top and some tabs beneath it. Click on the hardware tab. On the bottom of the window there will be a drop down menu for different sound profiles under "Settings for the selected device". On the dropdown menu, you will see all the available outputs for your sound card.
To get sound through my headphone jack, I just clicked the profile "analog stereo duplex", and turned out the volume was muted for it. You might not have the same profiles as me, or even the same settings menu, but if you do, just try some sliders on the different profiles and see if you can get some sound ;)
good luck! Hope this helps!