How should I handle this iPhone problem?

Ok so my iPhone went out of charge and it's been out of charge for a few days now. I tried charging it, but it won't even turn on. Occasionally it makes noises like an incoming text. Or when I press the home and power bottom at the same time, it occasionally makes a screenshot noise. I've tried charging it and pressing the buttons for 10 seconds.

Leave it charging for some 4 hours. They tend to die and won't turn on until charged for a while.

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