Heya sluvy4tune,
Let me get this straight.
Your IPOD is failing to power on when you turn on power to the unit - right.
As you have rightly stated - running down your battery is the most likely cause of this undesirable phenomenon.
As well in all likelihood, the battery ran down due to the failure of the charger unit.
Assuming these are the actual symptoms you are experiencing, my best guess is your IPOD charger has simply failed.
If I were you, I would simply find a known working charger for a similar IPOD (maybe a friend of yours can borrow you one) and try to charge your IPOD with that. If it works then you have isolated the problem to your failed charger. You can also go a step further to verify that your charger fails to charge your friends IPOD. Now how is that for an online diagnosis

You do that and get back.
Good luck,
brume