iPod classic has no sound output

Since the song is playing normally but there’s no sound through either the car or headphones, I’d first rule out a simple software glitch.

Try resetting the iPod: hold the Menu and Center buttons together for about 10 seconds, until the Apple logo appears. This won’t erase your music.

Also check that the volume isn’t limited under Settings > Volume Limit, and try another pair of headphones if you can.

If there’s still no sound from either output after the reset, that starts to point more toward a hardware problem with the audio output circuitry rather than syncing or the music files.

Glad you got it working, and thanks for posting back with what fixed it. That may help someone else with the same problem.