This is a problem that nobody seems to want to answer, but it's a problem that comes up again and again with my system too - a VGN-FZ290 laptop.
I'm not sure why the computer occasionally shuts down the Headphone jack, but it does. The solution to the problem is mind-numbingly simple, but since it's generally several months between the the problem's reappearance, I always forget how to turn it back on, I always go surfing for solutions, and always there is nobody who will post the answer.
So for all the other poor frustrated users out there with this same glitch, there is nothing wrong with the headphone jack, it's just been disabled by the system. Assuming you've got Windows Vista or 7 (or later) installed, here's one way to turn it back on:
1. Right-click on the speaker icon in the taskbar at the lower right of your screen (or left click the icon, then "Mixer" at the bottom of the pop-up) ;
2. Select "Open Volume Mixer"
3. Under the Headphones icon either click the speaker icon with the read circle-and-slash through it, or just move the headphone's volume slider to max.
This can also be done via going to Control Panel -> Hardware & Sound -> Sound, then making sure the Headphones option is enabled in the Playback tab of the pop-up window.
If none of that works, the Headphones option is greyed-out and doesn't allow you re-enabling it, it's trickier.
What I did in that instance was disable both of the other two - the Speakers and Digital Audio HDMI options, then plug in the earphones and let the Windows Troubleshooter window pop up. When (if) the Troubleshooter automatically re-enables the headphone jack, go back and re-enable the other two. After that, the system should detect headphones when they're plugged in and automatically mute the system speakers.