Mac mini built in speakers do not play all of sound
it a little bit odd, but the Sound preferences in System Preferences only shows the controls for the currently selected device.  If you plug in headphones for example, it only allows you select and alter the sound preferences for the headphones (and doesn't even show the internal speakers)

It maintains different sets of preferences for each output type.

Unplug your headphones, then open the Sound preference pane and see if there is anything amiss in the sound output tab.

(also please let us know if you have any software like Hear or Audio Hijack Pro that might be interfering with your audio output but thats a long shot)