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