The Power button doesn't work or is broken
The power button (located on the right hand side) can be pressed down, and the tactile feedback can be felt. However this does not turn on the handset. When a hard reset is done (by removing the battery and placing it back) the phone starts for the first few seconds (showing the Samsung logo) and then proceeds to shut back down.
Problem has occurred before after dropping the phone, but hasn't come back until now.