There's also a chance the problem isn't with the jack or the headphones you're using but has to do with the audio settings of the device.....Just open up the audio settings on your device and check the volume level as well as any other settings that might mute the sound.
This can be caused by (depending on the laptop model, you didn't say what model you have) a faulty backlight power inverter, faulty backlight power cable, faulty lid switch, faulty video cable or faulty screen.