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My brother He was trying to replacement the battery on my iPhone 5s he plug the charger cable And then plug the battery cable in phone when I try turn on the phone show me apple logo then black/blank screen

Most likely a bad battery. Did he try the old battery instead of the replacement battery? Does the iPhone turn on to apple logo at least when you plug the battery in then the charging cable after? If not then U2 Tristar charging ic chip on the logic board is at fault and needs to be repaired by a microsoldering tech.

Hi, If he was trying to replace the battery, and the only thing that’s showing when you plug charger in is the Apple logo then going off, then it is more than likely a faulty or damaged battery, as the phone isn’t seeing the battery, try another battery and this should solve your issue. :-)