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Just replaced a new battery for my iPhone 5, but the battery percentage won’t increase while charging. So I changed another new battery and has the same result. I tried to turn off the phone and charge it, and the iPhone turns on every time i plugged the power in. any one know what has happened to my phone?

Potentially the dock connector. Try unplugging the dock connector flex and reseating. If not you could buy one and bypass the installed dock just to test it quickly. Otherwise likely to be the logic board.