Hi there and welcome
Is it actually starting up though? Can you get to settings on it?
ok, can you do the following please
First, turn off the phone by using the Power button.
Now press and hold together: Volume Up + Home + Power button, until you see Samsung logo.
Can you then get to the recovery menu this way?
It is the internal mainboard that has faulted. This now confirms it
I am really sorry about this and you are going to have to return the phone to have this replaced. It will be covered by the warranty if this has not expired, and the replacement will be done at no cost to you.
I am really sorry about this, and if you have problems, or would like any additional information or assistance, please do not hesitate to let me know.
And if you can take a second to rate my service by clicking one of the stars at the top of the page, then submit, that would be greatly appreciated.