PC restarts at random intervals (probably solved?!)

i have no idea how to test them, unless i can swap parts and see which one fails.

actually i can't even do that, but it's what i've seen my friends doing xD ¯\_(ツ)_/¯

If it completely turn off out of nowhere then it is probably the PSU. If you have a demanding GPU (Usually amd GPUs) and you launch a game/application that requires you an high use of the GPU and your PC turns off then it could be either the PSU or the GPU.

In your case the pc restarts randomly and this could be caused by a faulty PC component like RAM or Motherboard. I think it is probably the RAM and I advise you to test it using MemTest86.

If the RAM doesn't have any problem then I advise you to "test" your pc daily and think what could be the faulty component and "test" it maybe using a game and seeing if it crashes faster than normally. I know it's a risky option because this could just damage more your already broken component but this is how you check a faulty piece in your PC.

If you are not sure what to do and you don't want to use any program or anything at all I always suggest to go somewhere near your zone where someone can check it for you. I know it looks a dumb it's the wiser solution.

Source: I had my first pc at 2 yo and I had all kind of problems (All the already mentioned problems as well) and I managed to fix them.

defrag will not check the sectors of a hard drive - you need to check for errors on the platters - voltages can be checked using the bios - and some windows progs I believe will allow you to monitor them - which is better if looking for a failing power supply - as for the temp issue, mine was fine in the hottest day as well, but every now and then the broken peg would cause the heatsink to move (it was very random and had nothing to do with temps of rooms, just occasional knocks of the tower or similar and the heatsink would shift and temp would spike)
for errors - go to drive - right click - go to properties tab - go to tools tab - go to error checking - scan hard drive (this is just a basic check though and not a full check)
hope you get it sorted soon :)

get "HW monitor" and open it up, then you can easily monitor temperatures

http://www.cpuid.com/downloads/hwmonitor/hwmonitor_1.32.zip

Well if money is not an issue i'd just take a risk and get a new psu (don't know how much watt you got now) good chances are it's just that. But you might try out some things from beforementioned youtube clip first though.

go buy New psu, and problem fixed ;)

At least half an hour, preferably over an hour.

Remove the RAM-Sticks and test with only 1.
Put them in different slots.

Test should take at least 1h

http://lmgtfy.com/?q=Kernel-Power+bugcheckcode+278
You didn't say anything about BSOD's, but you should be getting them.

Did it start around the time you updated your graphics cards and it's an nvidia? Use DDU to remove everything and then install a bit older driver.

Bugcheck 278 = 0x116 = VIDEO_TDR_ERROR - "This indicates that an attempt to reset the display driver and recover from a timeout failed."

Probably, update the video driver, downgrade the driver (if latest update doesn't work), or remove and reinstall the current driver. Update the firmware, downgrade the firmware (if latest update doesn't work). Ensure you're using the latest BIOS for your motherboard as well. If you're overclocking anything, stop doing so.
Do you have alternate video hardware you can try?

Warranty fix?

In my case I discovered it was the PSU when I installed a program from the CD that came with my motherboard that was called MSI PC Alert 4. It had it running in the taskbar, when suddenly it appeared on my screen while making a noise like a siren. This program also listed the PSU voltages, and the +3.3 voltage was in red because it had dropped below 3. I discovered that during high CPU usage it would start dropping and when it dropped below 2.70 my computer would restart.
Maybe you could try using a program like Speedfan to see if the voltages are normal or if they start dropping during high CPU usage, like it happened with my old PC.

no that's not what is meant, go

 C:\Windows\minidump\

is there something?
or file:

  C:\Windows\System32\memory.dmp

are memory dumps activated in the window here:

https://www.tenforums.com/tutorials/69012-enable-disable-bsod-automatic-restart-windows-10-a.html

View attached image.

You're getting a BSOD but you can't see it because of the restart itself. I was going to post the same tips than Tristar and Lugum. Once you can see the BSOD message, it will be easier to troubleshoot.

Yeah, you totally wanna replace that with a quality PSU.

Anything with the Turbo X brand is crap. You'd better buy a good PSU. I hardly buy any hardware from Πλαίσιο anymore. Too much Turbo X crap that they want to sell to their customers.

You are sure it's not overheating, so it's just something to rule out.
It can be software forcing re-starts. Possibly due to updates being installed.
You can check that your power source is sufficient for the newer parts...

Might as well do this and a full malware check.

I didn't even think of checking the cables, to be honest

Most people don't. When I come across issues like that, I start at the wall and work my way through the PC.

I've found more than one faulty cable so it's not that strange, those parts are very cheap and sometimes you can get some for free so checking the cables and the PSU first is a good advice. To check the PSU just borrow one from someone you know (make sure it fits your PC power specs) and connect it to your computer, you dont have to remove one single screw just unplug the cables and plug the respective ones of the other PSU, dont bother installing the PSU inside the box, if your computer behaves the same way then the PSU is not the cuprit and you can reconnect everything as before.