My phone is not turning on

Today morning I got a call but when I pressed the power button to make it silent, it continued ringing till call got disconnected, I couldn't receive the call.

Now I guess it got turned off and not able to restart. I also tried to hard reset by volume, home and power button, but boot menu didn't come.

I want to save my data before I can send it to a service center. Service center don't care to take backup and straight away flush the memory. Can anyone please let me know how can I take backup before sending to service center