What should you do if your headphones are not producing any sound while plugged into the headphone port.

As long as there is no obvious foreign objects/substances stuck in the headphone port, and the headphone jack can fit correctly inside the headphone port, then usually the issue can be solved just by checking the following settings on the chromebook. 

I will post a walkthrough video later but for now you can try the following:

  1. insert some headphones into the headphone port
  2. click in the system tray in the bottom right hand corner (time)
  3. Next to the speaker icon click the arrow  ">" 
  4. Under the "output" settings select "headphone" in the list
  5. Now you test out the headphones 

To test the headphones I usually just turn on "ChromeVox (spoken feedback)" from the same settings menu as mentioned above or on your keyboard do CTRL + ALT + Z to enable ChromeVox (spoken feedback)