Just an update at this point because I'm not sure if it is fixed yet. Like I said at the beginning, it is intermittent.
I updated the BIOS - AMD Turks XT Radeon HD 6670 (M208) v.8.812, A00 7.12.0.7700 and this did not change the lack of sound.
I updated the first chipset update Intel AMT HECI v.7.0.0.1118, A00 1/9/2011 and after plugging in the headset and removing, the sound worked from 6/17/13 to 6/23/13 and then stopped.
I rebooted the PC and the sound worked for an hour and then stopped again.
I updated the second chipset Intel Utility H67 v.9.2.0.1015, A00 today and the sound is working again. This is the end of the suggestions you made, since I updated the audio driver earlier (see post above).
I will update this again in 2-3 weeks or when sound stops again, whichever comes first