Dell xps l502x laptop won't boot past Dell

Hello, I got my Dell xps l502x in the mail about 2 weeks ago, it has been working fine for all my Programs even games. But yesterday I was playing civ 5 for about 30 mins then my laptop randomly shut down. I tryed to turn it on using the power button but nothing happens. So I took out re batter and ac cable then plugged just the ac cable in, it then started to boot but shut down completely right after the Dell screen loading bar goes across. I tryed holding and pressing f12 but nothing happens it just shuts off. I would also like to point out it doesn't start when I press the power button but only starts when I first plug in the ac cable or when I just insert the battery, but never when they are both in. My battery lights show fully charged, and the ac cable is lit with the blue light, but still will not get past Dell screen. I thought it might be overheated, so I waited till after school the next day. I tried it then, and it booted windows and got to my login I went to go tell my mom that it was fixes.l, got back and it was off again and having the same problem. Any help is greatly appreciated, and thank you in advance.