IPhone 4 won't charge?

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(?)