I would recommend taking a look at the troubleshooting steps found in the article below.
The headphones don't work
If your iPod's headphones don't work or have static or garbled audio, try connecting them to any other 3.5 mm stereo headphone jack, like the one on your computer. If the issue with the headphones persists, replace them. For an iPod under warranty, you can order a replacement online. Otherwise, check out the cool headphones at theApple Online Store. If the issue appears to be with the iPod, try resetting it. If that doesn't work, then restore iPod with the latest iPod software using iTunes 7 or later.