I had the same problem. The only "Sound" that worked without headpnones was "Ringtone". With headphones plugged in everything worked fine. After sweeping up from the bottom of my iPad to check the volume setting, I happened to click on the "Airplay" icon and found that it was playing to a set of remote speakers when the headphones were not plugged in. I do not know how Airplay got set to the remote speakers, but that was my problem.