Why does my Macbook Pro gets a black screen out of where and shuts down?.

Hello,

So i've been getting this issue where out of nowhere my Mac gets this constant unresponsive black screen whilst making the fan overheat?. I'm actually writing this from my Mothers computer.

It started one night where i was playing this "Heavy Usage Game" with a wired keyboard and mouse with my Magsafe 2 charger connected. After some time i closed off the game, disconnected the keyboard, mouse and charger then out of where my Screen turns black and shuts down? i thought ok this is just some little glitch let me restart. I turn it on and go search the web then this time its get an unresponsive black screen with the keyboard lights still on and and the fan starts to overheat? i decide to just watch what happens and after 20 minutes nothing changed. I turn it off and do some research, The Magsafe 2 Charger i had was some what "Faulty" but still worked just fine although it had a rip on the cable which was duct taped. My Mom and me agreed that this isn't safe and we need to get a new one. So me and my Dad go to the apple Store and explain to the Guy that my Computer was shutting out etc and he asked what charger did i use? i said i used a 60 watt charger on my Macbook Pro 15 inch and so did my Mother with her 13 Inch Macbook Pro. He then said overtime the 60 watt charger can damage the "AC pins" and the overall battery because of the low watt charger. I knew that my Mac needed an 85 watt charger but the funny thing is believe it or not i received this 60 watt charger when i bought my Macbook Pro 15 back in late 2013. And yes i bought the Mac from the Apple Store. So then i told him that and he was shocked. I bought the Chargers and came back home to Charge my Computer. Nothing changed although it charged my Computer faster. I do some more research and it turns out there are A LOT of people with the EXACT SAME issue that i have. I have reset the SMC (Shift/Ctrl/Option/Power Button) multiple times including the NVRAM/PVRAM (Option/CMD/R/P/Power Button). I've booted my Mac in Safe Mode more than once, I checked the system report under Power and my Battery Condition is "Normal" my Mac has no issues charging and it lasts a very long time before shutting down also my Battery Cycle is 1612.

My Specs are:

Retina, 15-inch, Late 2013.

Processor: 2 GHz Intel Core i7

Memory: 8 GB 1600 MHz DDR3

Graphics: Intel Iris Pro 1536 MB

Software: OS X 10.9.5 (13F1911).

I decided to scan my Mac for any viruses twice, Didn't find anything. I Verified Disc Permissions and the results were clean nothing found, I Repaired the Disc Permissions just to make sure. I then downloaded Coconut Battery and the Maximum Charge is 100% whilst the Battery Capacity is 85%. I deleted some Old Applications or Apps that even had the slightest glitches and i deleted the "Heavy Usage" Game i was playing which was 16 GB. I then decided to do the AHD (Apple Hardware Test) I turned my Mac off and pressed D, The test results were "The battery will need to be replaced soon. It is functioning normally, but holds less charge than it did when it was new. " everything else seemed to be fine. I have a solid amount of Space on my Computer and i kept it Clean for Years now and this all seems very very strange. Could this be the Motherboard, CPU, Fan, or Battery? i don't know. I red somewhere someone had reset his SMC and did a drain and recharge cycle to keep a pattern? maybe i'll give that a go.

It would be great for someone to give a Solution to fix this!. Last option i'll go to the Apple Store.

Regards,

Daniel.