How long have you left it to charge? How are you charging it? Via a USB port on your PC or via a wall adapter? Have you tried using another cable to see if that makes a difference?
Note that it could take up to 30 minutes of charging before the iPod shows any signs of life. Even then a hard reset might still be required to get it to boot up. To do this, make sure the hold switch is in the Off position, then press and hold both the Select/Center and Menu buttons together long enough for the Apple logo to appear.