Isnt on

1. Is the battery charged? (Have you checked that your charger and the cable are both working correctly?)
2. The Classic has a physical lock switch (on the top edge) which, if turned on, will prevent the power on procedure from working. Have you ensured that the lock switch is off?
3. Have you tried resetting the iPod? If memory serves me correctly this is accomplished by turning the lock switch off and immediately press-and-hold the centre button and the menu button until the Apple logo appears
4. How long since this iPod last worked? Has it been sitting in a drawer without any power for several months?

If it's been sitting there with the battery drained for two months then the very first thing to note is that once you plug in a power supply it can take up to thirty minutes before the iPod shows any signs of life. Then you should leave it to fully charge.

If it shows no signs of life after about an hour, that suggests that the battery has failed. Apple no longer offer a battery replacement service for that model, so you would have to find a third-party business local to you that knows how to change it for a new one (if that's what you choose to do).