First off, ensure that the headphones work by plugging them into another device. If the headphones do work, the audio jack may need to be cleared of any dust or particles that entered the opening. Try looking into the opening to see if there are any objects blocking the connection. If it is still unsuccessful, you may need to replace the audio jack using the replacement guide.
Your device’s battery might be dead. You may simply need to charge the device, however if your device has been plugged into a charger and is still not getting a charge, you may need to replace either the charger, or the battery, or both.