I'm on a laptop, and a few days ago my headphone jack stopped working. I can verify that the problem isn't my headphones. I've tried 3 others on this laptop to no avail.
Right click on the volume icon the bottom right corner of your screen and click "Playback devices". Right click and click "Show disabled devices".
See if when you plug in the headphones, see if it says "disabled". If it is, right click Headphones and enable it.
My headphones don't show up on playback devices. I only see speakers, and that's it. Yesterday it my headphones worked for a few hours, and even though they were working, the only thing in playback devices was stereo.