iPod only shows an Apple logo and doesn't start up. This means that the firmware in the iPod won't start up. It is the equivalent of hanging at the Windows logo screen on your PC.
You have a just one depressing option. You reset your iPod by:
# Pressing the three fingered: a) turn the hold on and off, b) press together Menu and Select and then finallly while it is starting press Menu and Play
# This gets you into a low level disk mode which should hopefully boot the iPod, you then connect to your PC and run iPod Updater. Hopefully you can just Update (get a fresh copy of firmware) rather than Restore (wipe the whole thing including all your music).
# If it won't even come up in Disk Mode, off to the Apple store you go.