I am not the individual who initiated this query but I did have the same issue with my Dell Inspiron 5547, where it wouldn't turn on after a power button shut down.
I followed Hema's instructions by removing the battery and charger and then holding down the power button for a few seconds, and then putting back the parts. It seemed to have done the trick... At least for now. Is this just a temporary fix?
While doing a Google search for a solution I seem to have encountered a number of people who experienced the same issue. Can you also explain why this happens with this particular Dell laptop? Is it a model flaw?