Almost always configuration, and the reason is a piece of hardware behaviour people do not know about: one physical jack is often several possible outputs, and something has to choose.
Modern audio chips have a small number of internal converters wired to a switching matrix. The jack can be a headphone output, a line output, or on many machines a microphone input, and the driver picks based on what it thinks was plugged in. That guess is what fails.
So the diagnostic order is:
- Look at the output device list while the headphones are plugged in. If a new device appears, the machine detected the plug and the routing is wrong, not the hardware. If nothing appears, detection failed — which is still usually configuration.
- Check the jack's assigned role. Most sound systems expose the connector's function as a setting. If the jack is set to line-out or microphone, headphones will be silent and nothing will look broken.
- Check for a second volume control. Many chips have independent controls per output, and the headphone one is frequently muted separately from the main one. This is the single most common cause and the most invisible.