IPhone 4 won't charge? When I plug it in, it doesn't charge. But when I turned it off and plugged it in, it turned on, but didn't charge. What's wrong with it? Is it the charger or the phone?

UPDATE:
the charge is going up, but it doesn't say it's charging... I don't know if that makes sense. It doesn't vibrate when I plug it in, it doesn't have the charging symbol, and it doesn't have the charge on the lock screen, yet it's charging(?)
most likely your 30pin dock port is full of dust and dirt, take a tooth pick, and verry carefully remove any dust that may have been stuck there.