Why won't my headphone jack work?

Assuming you are using functional headphone. First try turning the device off then back on, if this fails, try checking the volume settings on the device. A factory reset may be your best option before taking the device apart.

If you do take the device apart and are looking for the fault. The headphone jack itself could be damaged internally from use, or the connections from the jack to the motherboard could be faulty or damaged.