Randomly restarting, wont charging, and general mass

My old iPhone 4 started to act like a wirdo, sometimes he don't want to get charge when plugged, sometimes he randomly shutting off, even in a middle of a call, sometimes the percentage that shown hes nothing to do with the actual amount of juice, and the worst of all, almost always he shutting off when i plug out the cord and i need to turn him on again by pressing the power button.

and i just replaced the battery. didn't help.