There are two possiblities here.
Either; the iPod's battery is (was) fully drained and that's why it doesn't turn on. In this situation, once it's plugged into power, it will not show any signs of life, possibly for thirty minutes or so. When it does show life, it needs to be left on charge so that it has enough power to run once it's unplugged.
Or; the iPod is "stuck" doing something and cannot move on until it has finished. (I have no experience of this with my iPod Touch, but it has happened on my Classic.) This "stuck doing something" may mean that the iPod cannot turn the screen on to let you know what it's doing! So by plugging it into power, it has enough power to keep trying to finish what it cannot finish! (Are you still following this?) 😉 The solution in this case is to unplug the iPod and leave it alone until it has run out of power. Once that happens, the iPod cannot continue to "try and finish" the task - because it has no power. And when it does get power back, the very first thing it should do is set every switch, ciruit and thingy (a non-technical term, you will notice!) to a known condition, which means it should then work again.
*To summarise:* if leaving it on charge does nothing, leave it unplugged for a few days (so that the battery drains down fully) and then plug it in to power, wait, and see if it springs into life.
Phil