No sound except with Headphones on MBA The sound output is not stuck in digital mode, actually the output is stuck in "headphones mode". It works when the headphones are plugged in. 

Plugging in or replugging the headphones does not change mode from headphones to digital, it stays on headphones. It does not solve the problem either. There is no red light. Instead there is a white light. Blowing at it failed to work.
I had a similar problem when I used an older version of AirParrot, it would not switch the Audio back to Built-In. Had to manually go into preferences.

If you checked the System Preferences -> Sound -> Output and System Preferences -> Sound -> Sound Effects and it does not show Built-In option when headphones are out:


Make sure there's nothing stuck in the AUX port, no dust pieces or
anything. Or is it USB headphones?
Then I would reset PRAM and NVRAM to clear your computer's
inner caches. If it resets it and makes it right until the next time
you plug teh headphones in and  it happens again, try different
headphones, does it do the same?
Try to get your hands on another bootable copy of Mac OS, could be
you may need to reinstall the System folder, which should not
affect any of your data. Just select this option when you do a Restore (but backup your system anyway).


If still the same, I would bring it in to Apple store since they will diagnose it for free.