For some odd reason the sound does not always work properly on Linux Mint 13 XFCE. In my case it worked for a few weeks then stopped. It turns out this is not so much a bug but a settings issue which can be fixed quite easily. Also before going further please check that you have not muted your audio settings.

  Go to software manager and download “Pulse Audio Volume Control”
  Open it from Menu->Settings or type “pavucontol” into the command line
  Click on the “playback” tab and check it is at 100%; this may be higher than needed but atleast makes sure you have volume coming out.
  Go to the “configuration”. You should see two tabs set to profile.
  Set the top  ”built in audio” profile to “off”
  Set the lower one to “Analogue Stereo Output”
  Close the pulse audio volume control. You should now have sound.
  You may need to restart the computer if you do not yet have audio.

It is always worth checking that your computer has not set your sound output to HDMI, this can happen after you have used an HDMI monitor. Therefore always check the sound settings which you can find by clicking on the sound icon. If your sound has changed back to HDMI then you may need to go through the steps above again.