Hey A M! Sorry to hear about your problem, but i am thinking that your LCD went out. From what i understand, you said the screen just turned black then eventually it just turned off. It doesnt really make sense that you just slept on it and the LCD went out but if you take it to a repair shop, they can test a new LCD and see if it starts working. As far as it getting hot, it might just need to chill out for a minute. Let it off the charger for a couple hours or so, then when it cools down, try to make sure it at least has some charge. Then take it to your nearest repair shop and let them know what happened and that you think the LCD might have gone out. They dont have to do too much work to test that. to me that really seems like thats all it could be. If that doesnt work, you can send it into apple and have them take a look. Or i even do repairs through eBay, if you would be interested in that. My success rate is pretty high, and if your in the U.S, turn around time is great.
I hope this was of some type of good help. Any other questions you might have for me please ask!