I don't have an S6, but if the phone allows you to remove the battery, and the Sim card I would do that and then attempt to power it on.
If that doesn't work I would then try to power it on while plugged into the charger. If it turns on while plugged into the charger that will tell you the battery never charged and simply died which may be cause for a new battery.
If that doesn't work I would also try to power it on in safe mode; hold the volume down key while pressing the power on key.
If nothing happens at all trying any of these...I'm out of ideas and would at that point go into the store. Your device should have a 1 year warranty on certain defects.