Sudden shutdown problem

I have an issue with my computer. Over the course of this last year, it has been switching off randomly, as if the power button had been pressed for several seconds. When the problem started it happened maybe once a month, then once a week and eventually, it became so frequent that the use of the computer was impossible. I had taken it to a computer repair shop but they were unable to diagnose the problem and after this the computer went unused in my room for several months as I was busy with university work. I had noticed a series of factors that seemed to increase the chance of the computer switching off. The problem seemed more likely under load, before the computer became completely unusable I could play games with low requirements such as league of legends and mount and blade, but when I played more intensive games like TW: Warhammer and Hellblade: Senua's Sacrifice the computer would crash within 15minutes of starting up the game. I had noticed that my CPU was getting fairly warm when playing these games 70-80 degrees C, so I replaced my stock CPU cooler. However, whilst this did help to lower my CPU temperature it did not stop the computer turning off. Then within a few weeks, the problem had become so frequent that even watching youtube in chrome or being on idle was enough to cause it to switch off.

After several months of being unused, I decided to try it again and to my surprise, it worked, I was able to play Hellblade for an hour without it switching off and I for about 5 days I could play League with no issues. However, after this period the problem reappeared, at first it happened once on the first day. and after a few days, it was back to being almost unusable. At this point, I am lost as to what to do, I believe that the cause is one of 3 things the CPU, PSU or mobo. I do not believe it is an issue with my ram as I have tried both sticks separately and the problem persists.
I made the PC in Jan 2015 and the problem has only been ongoing for about 8 months, so do not believe it is a problem with my build which I will post at the end. The problem also occurs more frequently at higher temperatures and at load, however, I do not believe these are the sole causes as when it's at its worse at idle at 30 deg C it happens. I have noticed that sometimes after switching off the computer cannot be switched back on again, after pressing the power buttons the fans will spin up the lights will come on, but then a second later the fans stop but lights remain on. Then a few minutes later the computer is able to be turned on again.

I would be very grateful to hear your guys opinions, and whether there are any ways I can diagnose the problem as I currently do not have any spare parts to try and determine the faulty component this way, and I currently cannot afford to buy replacement parts without being more sure as to what exactly I the faulty component.

Specs:

>Intel Core i7 i7-4790K CPU (Quad Core 4GHz, Socket H3 LGA-1150)

>EVGA Nvidia GeForce GTX 980 Superclocked Graphics Card (4GB, GDDR5, PCI Express 3.0)

>HyperX FURY Series 16 GB (2 x 8 GB) DDR3 1866 MHz CL10 DIMM Memory Module Kit - Red

>Gigabyte Z97MX-Gaming 5 Intel LGA1150 Z97 express chipset (4x DDR3, 4x USB3.0, 4x USB2.0, HDMI, DVI-D, DSUB)

>WD 1TB SATA lll Desktop SATA Drive - Blue

>Samsung 850 EVO 2 TB 2.5 inch Solid State Drive - Black

>Silverstone SST-ST85F-GS - Strider Gold Series - 850 Watt (SST-ST85F-GS)

Sorry for the long read, just wanted to make sure that I included everything that might be of use. Thanks for reading.