Why is my computer not turning on?

My computer is 3 wks old. Yesterday I went to turn it on and it made the chime sound, but never turned on. Plugged it in and tried again, nothing. I let it sit longer but it acted like it wasn't charging because the green light never turned on. I checked the charger and it felt very warm as did the computer. I unplugged and let it all cool down. I re-plugged it in and it finally charged it all the way or at least I thought so. The light was green, but it will not turn on no matter what I have tried. What should I do next?