Before considering changing parts, start with something simple.
Make sure the power cord to your PSU is tight. Some times you may accidentally shift your computer a bit and that could result in your psu power cord losing contact. Make sure the power cord is in fully and use your hand to hold it in place in a centre position then try switching on your PC again.
If you computer does switch on, then it means that your power cable is loose and you need to find one that can fit snugly into your PSU so that it doesn't droop to one side. Alternatively, you can use cable tie or something to hold it in place/prop it up.
If you want to test PSU, then do the "paper clip test", look at the following link. But that one got to take out the atx 24 pin which can be hard to do. Make sure eco mode is off as well othewise psu fan might not spin.
https://help.corsair.com/hc/en-us/articles/360025085372-How-to-Test-a-PSU-Power-Supply-Unit