I had a similar issue battery wouldn't hold charge wouldn't turn on unless connected to the power kept restating etc had to send it to repair but they didn't state what was repaired. Try another battery or charging cable.
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Now: Samsung Galaxy S4 I9505
Rom: Omega Rom 13.2 - Simples | Der Kernel: Stock 4.3 Kernel MJ5
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Tablet: Nexus 7 2013 32GB