MBP black screen, then back to normal...?

Hello.

I have an Early 2013 MacBook Pro 15. A few days ago while playing a game, the temperature got so hot my system automatically shut itself down.

I tried turning it on, but there were no sound or anything when I tried turning it on (only a faint fan noise could be heard).

I’ve searched the internet and did SMC, PRAM resets. After I did that, when I started the system, I heard the starting sound, but the screen was still black (also, the keyboard and screens backlight and the apple logo on the back did not glow, etc).

So the next day, I took it the the Apple service center, then all of a sudden when the repair guy turned the system on, the Apple logo appeared! But, then screen went black (but I could still hear a slight fan noise). The apply guy told me that the board is likely damaged, and added that it might cost about $800 to fix, which I refused.

Then I came back to my house and turned the system back on, and now it seems like it's just fine (in fact I'm using this to write this post).

Can anyone please explain to me what might be going on? Should I be worried?

I want to add additional information (update)

The first time the computer shut down, I knew it was hot because I used SMC fan control, and it showed the computer reaching 95C.

The next time I ran the game, I kept it very cool, and the CPU temperature reached 80 degrees before shutting down.

However, nowadays, the computer shuts down even when I’m not typing anything or doing anything (ie not hot at all).

Then one day the computer didn’t even do the chime when I turned it on. So I did two to three consecutive PRAM resets (one reset for some reason doesn’t work), and then it shows the Apple logo and boots up. However, after I type my password, the computer logs in, then for no reason it dies (the fans still run though)

Also, I started getting the message ‘Your Mac restarted due to a problem’ when I turn off the system with the black screen (by holding the power button for a few seconds), then turn it on again.

Also, thank you so much for answering my question!