IPhone 4s battery won't connect to charge unless off?

My iPhone does not connect to a charge unless it is off should I buy a new battery? Like would it help because i got locked out of my iphone like 3 months ago and it says connect to itunes. But it can't connect to a charge unless off and it needs to be on to connect to itunes. Unless it doesn't have to be on. Does it? Because i have put so much money into the dang iPhone i had the screen fixed about 4 times. And yea I MISS MY IPHONE.

Thats not good

So you had your screen fixed 4 times? It sounds like you can't take care of it, who knows what damage you have done.