2 Methods to Test a Power Supply
Power Supply Tester (Recommended): Obtain standard power supply tester. Plug into the main ATX connection. Depending on brand, should signal voltages that are working and those that are not. Please note some power supply testers test for -5V rail (White wire). Many modern power supplies no longer use the -5V rail. If you do not see a white wire on the main ATX connection the PSU tester may signal that it is defective.
Paper Clip Test: Bend paperclip into U-shape so points are both pointing in one direction. Make sure the power supply is turned off and unplugged. Find main ATX 20/24 pin connection. Short the Black (ground) and Green (ignition) wires by inserting the pointy sides of the paper clip into the pins that black and green wires go. Please note there will be multiple Black (ground) wires. You can choose either one. There will only be one Green (ignition) wire. Once paperclip is in, you can plug back in and turn the power supply on. Power supply should boot and PSU fan should spin.