screen flashes then turns off

I have a kindle fire HDX 8.9 which is 23 days outside its warranty date. Suddenly today when I push the power button to take it out of sleep mode the screen will flash but then turn black. I have tried pushing the power button down and holding it for 20 sec to reset it I have done this 6 times and each time when I push the button again it will flash the kindle fire screen then go black. If I push the button again the start up screen will flash then go black. the volume buttons make noise when I push them and the charger makes a noise when I plug it in but the screen will not stay on. Please help. they want almost full purchase price to replace it and I don't have the money to do that.