Try holding down the power and home buttons at the same time for 10-12 seconds. After that, let go of both buttons. Then keep holding the power button until you see the apple logo.
It's called a hard reset, but none of your data will be erased. It just forces your device to power down, and then we can reboot it.
After trying the same multiple times, my phone has now turned on.
But still its home button has become a little hard, as in while trying to switch on or off the phone, a lot of pressure is needed.
So maybe I should show it to my local Apple service center?