Why does my iPhone 4 charge only when its off?

I had my iPhone 4 for a year and a half.
It's really cracked bad! I never had any problems with it charging but all of a sudden it stopped charging when its on, but when its off it charges. Could it be over heated cause I charge all night lots of times? It's not water damaged. I changed the charger, and the charger isn't the problem.

The problem is probably the battery itself. Try going to the Apple store and getting it replaced.

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