Will not power up after power outage
Sometimes before the power goes out, there's a power surge. Not always, but a lot of times.
This could be tricky, but worth a shot.
Look on the back of your power supply where the power cable plugs in. Look to see if there is a switch that's been flipped so that it's turned off. Some power supplies have breaker switches. If it's turned on, try a different outlet you know works. If that still doesn't fix the issue, then you may have a blown fuse.
Typically, there are only four screws on the back of the case holding your power supply in. Pull your power supply out and take it apart. Don't yank on anything. Look for the fuse. sometimes it's a clear one that you can just look at. Sometimes it's one of those annoying ceramic fuses and it's just white in the middle. To see if that's blown, there are a few methods.
First is to use a multimeter if you have one. Set it to Ohms (resistance) and put a probe on either side of the fuse. Doesn't matter if it's in circuit or not. (Still plugged in or pulled out.) If you see infinite resistance, that means the circuit is open and the fuse is blown. Be sure to replace it with the same kind of fuse. There are stipulations where another type/spec would work, but for the sake of simplicity, just getting the exact same fuse is alot easier.
If you don't have a multimeter, there are other ways of checking. The first one is a voltage tester. You can get these for a few dollars just about anywhere. Get a battery too. Doesn't matter what kind it is as long as it's not a button battery. Now you're going to make a circuit here. First, put the probes of the voltage tester on either side of the battery to make sure it lights up. If it doesn't, then either the battery is dead, or if you have a voltage tester with a LED, then you've got it hooked up backwards.
Once you get a good light from the battery, then it's time to test the fuse. Put one probe on one end of the fuse and the other probe on one end of the battery. Then have a wire going from the other end of the battery to the other end of the fuse. Or just push that end of the battery to the free end of the fuse. This is where it's super handy to have four hands. Again, make sure if you have an LED tester, that it's going the right way. May have to flip the battery around a few times to make sure it's all working.
If you've done this and the light is on, then your fuse is good. If the light is off then the fuse is bad.
If the fuse is good, then you've got bigger problems.
If you don't have a multimeter or a voltage tester, then there's an even cheaper way to test a fuse. Get a 9 Volt battery. Touch one end to one of the metal ends of the fuse and slowly touch the other terminal to the opposite end of the fuse. If it's a good fuse, you will see a spark. You may have to turn the lights out and put on your grandpa glasses to see it. If you can't for the life of you get a spark, then most likely the fuse is bad. Or the battery is dead, again. Make sure it's either new or out of something that was working at full power at the time you pulled it out.
I really hope for your sake the fuse is blown. That's the cheapest easiest fix for this problem ever.
If that's not the case, let me know and I'll walk you through how to test your power supply without needing the computer to turn it on.