Firstly, I would check the physical cables connecting the PSU to the wall is okay, they are quite cheap and can be found at most stores. You should also try a different power outlet.
If this doesn't change anything, have a look inside at the computer itself, make sure the cables from the power supply leading to the motherboard are all fully connected, this includes your CPU connector, motherboard connector (the big one). GPU connector etc. Also make sure that cable connectors are not touching the metal inside of your case (if this applies to you) as this is known to create a short and the power supply wont start.
Next, look for any kind of physical damage, a bad PSU could have melted some plastic on a connector either on the motherboard or on the PSU itself, this can be a tell tale sign of something going wrong.
I would recommend to test the inside of the PSU but if you aren't experienced do not open up a power supply as it can be detrimental if it goes wrong. There are plenty of videos on youtube detailing the process of how diagnose a power supply but once again I DO NOT recommend unless you are confident and experienced in doing so.
Other things you can try is bread boarding your system, take out as many components as possible as see if you can get the computer to run on as little as possible - this would be: Motherboard, CPU + Cooler, one stick of ram and the PSU connecting to these components. If nothing else works, check the warranty on your PSU and see if you can get a refund. Don't accept a replacement if your budget can handle it, instead spend the refund and some extra cash on a better power supply. If that one has died I wouldn't recommend getting the same again.
Let me know if you need anymore help and good luck
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