iPod Help

I have a 4g video ipod 30 gb and my battery life seems to be inconsistent. Sometimes it doesn't want to turn off. Or even though it's fully charged it fails to turn on. When this happens to me the apple sign appears then the whole picture gets stringy. Even if I plug it to a wall charger it still doesn't turn on, the most it will go to is a lit up apple sign then it dies. I plugged it in to the computer: it had a message like Please wait, very low battery even though i had it charging for 3 hours straight. It seems that i will need my computer every time i would like to use my ipod. Can anyone help me out? I am desperate!!