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It is possible that the battery or internal board has failed. Please note, I can only give you instructions to fix the problem only if it is software related and I will not be able to fix this is if it is hardware related. Please don't rate me bad or poor if you are not satisfied with my service. You don't have to rate anything if you are not satisfied.
First lets try to soft reset. Press and hold down the Power button and Volume Down button at the same time for until it shows the Samsung logo or for 20 seconds. This will force reboot if it is a software glitch.
If that didn't work, then connect the phone to your computer with the USB cable and then hold down Volume Down and Power button for 20 seconds. This will also force reboot it unless it is a major hardware issue.
If this is S5, then remove the battery and put it back. See this video --> https://www.youtube.com/watch?v=V1MDGQzNMYI
You can't remove the battery if it is S6.
Please let me know how it goes
You can also hold down the following buttons combinations to force reboot it. Try the following combinations with and without connecting to computer.
Volume Up, Home and Power for 20 seconds.
Volume Down, Up and Power at same time for 20 seconds
Volume Down, Home and Power button until it shows Downloading screen.
Let me know if any of the button combinations boot into any screen