Chosen Solution
My iPod is fully charged, but when I turn it on it turns itself off
The cells in your battery could be dead. If the iPod shows full charge when plugged in, thats because what little cells you have left to charge take very little to fuel up. However, with a small amount of working cells, this isn’t enough to keep the iPod running. Since I trust hardly any other suppliers other than iFixit, i would suggest claiming a warranty service on it.