Thanks everyone for their inputs. I was planning to try the magnet trick but when I read about the flicking / tapping thing, I tried that first.
I just tapped the power button with the index finger good 5 times, sometimes so hard that the button got pressed. And then I tried to power it on without any cable connected. Boom, it booted up!!
Earlier, I was facing the same problem as many; the phone was not starting at all, however many buttons you pressed in whatever all combinations. When plugged in, it was rebooting at the Google Logo without any button being pressed.
Hope this would be helpful. Thanks all. Made my day!!