To troubleshoot a computers power supply, you can begin by checking the physical connections: ensure the power cable is surely plugged in and the PSU switch is on. You verify the wall outlet or surge protector is functional using another device. Inspect the PSU for signs of damage like a burned smell or bulging capacitors. Also, listening to for unusual noises or A lack of fan activity could be the culprit. I always like to ensure and rule out any other components like the motherboard or power button before replacing the PSU. Make sure to unplug the system when inspecting or handling internal parts, as this is a safety feature! These are some of the basic methods I use to troubleshoot this particular issue and overtime it becomes like clockwork.