Do you know if the battery might be drained? What model/generation of iPod is it?
Sometimes, when the battery is fully depleted, it may take a few minutes (up to 15 minutes or more, sometimes) before the iPod will respond again after being plugged in. The reason is that the iPod will not turn on if it senses there is not enough "juice" in the battery to sustain being on.
Try this... plug the iPod into the wall adaptor to charge and leave it alone for an hour or more. After an hour or so, try to turn on the iPod again.