No, not all phones require a sim. Without knowing the actual model you have, there would be no way I could tell if you do or don't have one.
If the phone is still under warranty, I would suggest you contact your carrier/provider or the manufacturer first. To see about getting it fixed or replaced. Before attempting anything that might void the warranty.
Now some things you can try that shouldn't void any warranty. First, try holding down the power button for about 20-25 seconds and then let it go. Next try plugging in the device and see if it starts to charge.
If the above doesn't work another thing to check is to make sure none of the buttons are stuck. Also, make sure your charger is working properly (try using it on another device if you can). Make sure also that nothing is in the port (dust, lint, food, etc.)