Hi,
Have to ask, you did try another set of headphones didn't you?
It may be that there is a faulty or loose audio output socket in the laptop.
Unfortunately it appears as though the socket is directly mounted onto the motherboard.
Here is a link to the [http://h10032.www1.hp.com/ctg/Manual/c03593268|service manual] for your laptop. On p.62 it details the necessary pre-requisites and then the procedure to remove the systemboard. You may not have to go this far to initially prove whether the socket is loose or not.
If it is deemed to be faulty then you will need to have the necessary SMD (surface mounted device) soldering skills and tools to remove and replace the socket.
If this seems to daunting for you to do, contact a laptop repair service and ask for a quote to repair the socket.
If you really wish to use headphones and a repair is not an option you could try this [https://www.amazon.com/Sabrent-External-Adapter-Windows-AU-MMSA/dp/B00IRVQ0F8/ref=sr_1_3?ie=UTF8&qid=1491790774&sr=8-3&keywords=usb+sound&tag=ifixitam-20|alternative] solution.
Hopefully this is of some help.