So your using your computer happily, going about your business perhaps surfing the web, streaming video, playing games or just about anything else, but then suddenly screen goes blank and computer goes silent as though the power has been cut.   Strange... so you power it back on again and not long after the same thing happens again. What could be going on here?!

First thing is to decide just how random the powering off is, can it happen any time at all, within a few minutes of starting the computer, or can it take several hours. This can be a good indicator as to if the fault is thermal, or if it's a faulty inside one of the components. Totally random symptoms would more indicate a faulty board and a thermal fault would be indicated by the fault being produced when they computer is under high stress or been on a  long time.

Well, let's go through the components inside the PC, and which of them could be the problem.

1: Case - Modern computer cases are designed with airflow in mind, much like a race car is tested in a wind tunnel, computer cases are designed to move air round the inside of a computer in a way that helps promote system cooling. You should always operate your computer with the sides on and the case secured.
2: Power supply - Sounds obvious but a problem of losing power to your computer can be a faulty power supply unit.
3: Motherboard - When I started my first job in IT a little over 20 years ago, a colleague referred to a motherboard as "the root of all evil". In the case of any kind of strange fault the motherboard often  the culprit. With a computer powering off randomly, while maybe not the most likely of the system components to be at fault, its defiantly not something that can be ruled out. Especially on some models of laptop that have a tendency to cook the motherboard chipsets  over time.
4: Processor - The CPU is among the more reliable of computer components, it's rare that a CPU  fails but not unheard of, though not the likely cause of this particular fault.
5: CPU Heat sink - The heat sink and fan could be the cause of a powering off problem, either faulty clips holding the heat sink the CPU, or the fan itself could be faulty and providing adequate cooling.
6: Case Fans -  Modern desktops and laptops tend to have at least 1 case fan which if not functioning properly can cause overheating which in turn can cause the power off issue.
7: Memory -  Again not very likely to be the cause of this particular fault but not something we can rule out.
8: Hard drive - Unlikely to be the fault.
9: DVD/bray player - Unlikely to be the fault.
10: VGA card - Very possible candidate for the fault here, the better graphics technology gets the hotter they run and so need bigger fans to keep them cool. Should those fans start to fail a VGA card doesn't tend to last very long.
11: Network card -  Unlikely to be the fault.
12: External peripherals, printer etc - Unlikely to be the fault but still possible.
13: Software - Unlikely to be the fault.

Troubleshooting
Ok So how do we diagnose which of these is at fault. We have 13 items here to rule out so let's starting with the easy stuff and progressing to more technical.

step 1:
Remove all external peripherals including all USB devices, try an alternative keyboard and mouse (unlikely to be the fault but you never know) if you have them and make sure that the sides are on the sides of the PC. Test the system and if not resolved move on.

step 2:
Enter the system bios and look for something along the lines of PChealth check, in here you will be able to check the speed of the fans and the voltages the power supply is pushing out. The voltages of each track shown from the PSU will be 12v, 5v and 3.3v,, you will see the actual measured about the PSU is giving out and usually any outside of tolerance will be displayed in red.  If either any of the fans are displaying a warning, or the PSU voltages are off this can be a good indication as to the faulty component.

Step 3:
If its a desktop open the side panel and check that all the fans are spinning, on a laptop you can run your hand around the grills to check air is flowing out. Fans to check are case fan at front, case fan at back, CPU fan and VGA fan if the system has one. If any of these fans are either making a noise or not spinning you have likely found the problem, also check the heat sink is properly attached to the CPU, a broken pin or clip on the mechanism that holds it down can cause this type of fault. Order/replace the faulty fan or heat sink or move on to next step if no fault found.

step 4:
Disconnect the DVD player and secondary hard drives, remove any PCI or mini PCI cards such as sound cards or network cards. If there is more than 1 Ram module remove all but one of them. If this resolves the fault reattach each of the removed components 1 at a time until we find the fault. Also remove the last ram module you left in and replace with one of the removed modules to rule out that final ram stick.

Step 5:
If by this point we still haven't found the fault we are looking at a CPU or motherboard problem, 9 times out of 10 it will be the motherboard when left with just these two. But in any case, this may be a good time to consider an upgrade, perhaps pickup a replacement motherboard and processor combo making sure that its compatible with your existing components you have in the unit.

By this point you should now have a working unit again.
 If you don't like the idea of following this guide, maybe don't feel comfortable going inside your computer or would just rather have somebody come out to look at the unit for you our onsite repair service is just £35 for call out and all labour costs.