Hi Zoe,
First, I would remove the SD card (if you use one) and the sim card. I had some corrupt SD card files that messed up the entire OS.
As a second step, try a hard reset. Maybe the Android phone is just stuck. How to hard reset: 1) press simultaneously power + volume down and keep them for 5-10 sec until phone, until phone display the Samsung logo. 2) press power and volume up simultaneously until it displays the debug menu. There is a slight chance for this to work in your case, but it is the easiest thing to try. If this works, then Reboot System now. If after reboot is the same, I would try again hard reset and then "Wiping data/factory reset", but this will erase your data.
Third, if the phone doesn't power up using the hard reset, I would try to charge it and check if the battery is warming. If it does, you have a clue that the battery might be ok.
There is also a way to re-install the Operating system by connecting the phone to a computer, but this is not applicable since it is visible for only a few seconds.
If the phone had a recent big fall or made contact with liquids, that might cause it. Or if you've noticed that the phone was warming up excessively during charging, it could indicate the battery or charging port.
I suspect the battery or the mainboard, but it is just my supposition. Let us know if any of this works and if you are interested in fixing it your self.
Good luck,