OK, first off, does anything happen when you click & release the Home or power buttons? As long as it's not shut down, you should be getting the lock screen when you hit either button.
Second, unless the 5th gen iPods work completely differently from the 4th gen iPods (which I have) or the iPhones (have iPhone 6, & the buttons work pretty much identically to my iPod), you don't use the Home button to turn an iPod on & off. The power button turns it back on.
Third, are you 100% sure that you actually turned it off in the first place? Unless you really messed with the settings, holding the power button down while it's turned on only brings up the red slider bar...& until you swipe that bar, it doesn't turn off...