Laptop headphone port not working

First of all check all driver/software settings, secondly ensure you have the latest driver for your sound device installed. Then proceed with the following:

Have you tried another set of headphones, did they work? Do you get sound from the internal speakers if nothing is plugged into the headphone jack? Do you still get sound from the internal speakers when you plug in your headphones?
If you answered yes to most of, if not all of those questions you are likely to need your jack socket replacing.

If you haven't tried another set of headphones, or other 3.5mm jack audio device, do it and let me know the results.

If the answer is no to any of the other questions please let me know which ones and I will try to offer more advise.