Check the charger isn't damaged, and check there is no dirt in the charging port which might be blocking the pins.
If you are using a computer, try a wall charger, or at the very least a different usb port, different cable if you have one. If using a wall charger, try a usb port and a different cable.
Try pressing and holding the power button of the phone for 30 seconds to force a clean shutdown.
Leave it on the charger overnight and see whether it starts to respond.
If none of that works, then you should take it in for repair. It should be covered by warranty.
I might add that if the charger/cable are ok then the charging light not coming on when the phone is switched off is a bad sign. But I'd try some of the other steps before going for repair, just in case