There are lots of possible reasons for your PC refusing to start up, ranging from the simple and easy to fix, to the much more complicated. However, whatever the reason, it's very likely that your files are safe. Unless something catastrophic has happened, there's no reason to worry about your data. If the worst comes to the worst and you can't get your PC to work ever again, you can still remove the hard drive or SSD and access it from another machine.
With that out of the way, let's look at the first steps if your computer won't boot.
1. Check for power supply issues
If there's no power getting to your PC, it won't start. The obvious signs of a loss pop power are that when you start it, nothing lights up and the fans don't start.
If it's a laptop, a loss of power could result from a battery that has completely run out of charge. So, the first thing to do is to plug it in and leave it to charge for a few hours. If that doesn't work, it could mean the charger is faulty, so, if you can try a different charger. If the charger has a power indicator, check whether it lights up when you plug it in.
If your PC is a desktop computer and doesn't start, check that it's not the plug socket at fault by plugging it into a different socket. If that doesn't work, it could be that the power supply in your PC has failed. If that's the case, you'll need to replace it. Before you do that, make sure that it is the power supply. If you can, remove the case and check that the power button is connected properly - a faulty button is much easier to fix than a power supply.
You should also try replacing your PC's CMOS (or clock) battery. This tiny battery supplies power to the motherboard so that it can store BIOS settings. It's essentially a watch battery and costs only around $10 replace. If your PC is more than three years old, it's a likely cause of your PC failing to boot.
You should also check your PC's power cable, by swapping for another one and trying again. Once you've ruled out the power cable, CMOS battery, and switch, and if you're comfortable using a multimeter, you should test the power supply. If it's faulty, have it replaced.
2. Make sure it's not a slow boot
Make sure your PC is not just really slow. It may sound ridiculous, but it could be that your PC is just starting up very, very slowly. So be patient and give it 15-20 minutes to make sure that there really is a problem. If it's installing updates or having trouble with autorun applications, it may seem like it's not starting up.
If autorun applications are causing your PC to start slowly, you can disable them. To do that, use CleanMyPC. It makes it very easy to stop apps from autorunning and slowing down startup.
3. Make sure your monitor or display is functional
If you can see that your PC has power, because the fans start up or the power lights come on, but nothing else happens, there are a couple of possible faults.
If you have a desktop PC connected to an external monitor, it could be the display that's faulty. Check the power connection to the monitor and that it's properly connected to your PC. Try disconnecting it and reconnecting it. If that doesn't work, try connecting a different monitor, if possible. That way you'll be able to either determine it's the monitor's fault, or rule it out.
If you have a laptop, or if you've ruled out the external display, it could be that your PC is in sleep mode and is having trouble waking. To check that, shut it down completely and restart from cold. To do that, hold down the power button for 5 seconds and then press it again to start your PC.
4. Eliminate external hardware
If none of the above solves your problem, and you have external hardware attached, one of those peripherals could be the culprit. With your PC completely shutdown, disconnect everything - except keyboard, mouse, and display, if you're using a desktop. Try starting it again. If it starts up successfully, shut it down and reconnect one peripheral then restart. If it's ok, repeat with another peripheral. Keep going until it fails to start, then you know you've found the problem.
5. Reset memory modules and internal components
This step isn't for the faint-hearted, especially if you have a laptop. But if you know what you're doing, you can open the case and remove then replace memory modules, your graphics card, CPU and even disconnect and reconnect the power supply to ensure that a bad connection isn't the cause of the problems. If you don't feel competent enough to do it yourself, you should ask a friend or colleague or take your computer to a repair shop and ask them to do it.
A few more reasons your PC won't turn on
If the issue is not related to hardware then you should probably check other reasons your PC won't turn on or freezes upon startup. Here are a few things you should try:
uninstall new software that may cause system conflicts;
clean corrupted caches;
perform thorough PC clean up to delete hidden junk files which prevent your PC from booting.
Fortunately, all these tasks can be performed easily with CleanMyPC - a tool for smart PC cleanup. It will help you deal with any kind of system junk, including cache and registry errors, and get rid of unnecessary programs. A regular computer cleanup will not only fix current issues but will prevent your PC from malfunctioning.