Testing audio on a laptop

"Things I'd do in order:

Verify that the headphones / speakers actually work on another device (may seem obvious, but you'd be surprised how often I myself forget to check the obvious first)
If your sound sockets are not integrated on the motherboard (for example a front-panel header of some sort), make sure the header is actually properly plugged into the motherboard, cables sometimes come loose unnoticed when replacing / adjusting something unrelated in the case
Go into the bios and make sure that the integrated sound hardware is not disabled there
Go to the site of your motherboard manufacturer and get the latest sound drivers you can find for your motherboard; ideally completely remove the currently installed drivers, reboot and use the install you downloaded to make sure there's no old remnants anywhere
Carefully check all the settings in the audio dialog of the motherboard; sometimes there is a way of switching between different output modes which disables normal sound output
Grab an Ubuntu boot disk, boot into this from the CD and see if sound works there (if this does not work, then odds are your hardware is just plain broken)

Obviously the idea is to check the audio after each step where you actually change something.

Hope this helps."