Laptop turns off automatically after 3 seconds and no display

At first everything is fine and the laptop is working properly delivering excellent performance. Then one day my brother is playing minecraft and it makes the laptop freeze and I have to force it to shut down. I thought it was another one those "easy solution problems" but it wasn't. When I turned on the laptop there's no display it was a black screen. I waited for the wi-fi light to turn white which means that the laptop is on. Nothing happened. Then I tried the 60 seconds power button trick, it worked the first time but then again I had the same problem. Then after that I tried the tilt the laptop to 30 degrees when starting it and it worked. I was really happy and I used that trick for about 3 months. But today nothing of that is working. I have tried tilting the laptop like I used to and there's no display, the lights turn on and the fan works but I'm stuck with this black screen, even the Wi-Fi light turns white which means it should bring me to the lock screen but there's only the black screen. I tried the 60 second trick, not working, connect my laptop to LCD, no DISPLAY. I tried to connect the laptop to LCD and there was no display before I found the 30 degree tilt trick so I'm sure its not the motherboard because there was no display on the LCD and I could use the laptop using 30 degree trick. Now I turn on the laptop @30 degrees tilted and there the fan makes this loud sound and laptop turns off after about 3 seconds. How do I fix this? Laptop was $600.

Are you sure your laptop's fan works correctly? It may cause of your cpu temrature

If it was CPU Temperature it would take on average 30 minutes for the CPU temperature to get high enough to trigger the shutdown.
This issue is common in laptops due to the fact that the video cable gets flexed quite a bit when opening and closing the laptop.

The reason it worked for a little while is because it repositioned the wiring so that it would work, this was only a temporary fix, it sounds to me like the cable has been severed completely.

It's a relatively simple repair, and should cost around 100.00 to fix at a 'mom n pop' computer repair place.