Try home, volume down, and power buttons for about 10 seconds.
Does the device vibrate at all when holding the power button to power it up? If it does not, it is more than likely going to need service. If it does but you don't see anything happen at all after leaving it for a few minutes. There might be an issue with the display. Either way, the device will to be fixed. On some solder and newer devices, the power buttons are removable. I don't know for sure if the S7's is, but perhaps check out JerryRigEverything's YouTube video on the device to see. If it is removable. Clean the backside of the button and make sure there is no gunk or anything interfering with the button making a connection to power up the device.
I see you've got some helpful steps above. Can you let us know if your phone powered up?