Before checking a fault in a mains-operated power supply unit, it would be safest to first:

When working on any mains-operated electronic equipment, the absolute first step is to remove the source of dangerous voltage. Turning off the power switch is not enough, as a faulty switch or wiring could still leave live voltage present inside the chassis. Unplugging the device ensures physical disconnection from the mains power grid. Checking the bleeder resistance or shorting filter capacitors are safety steps you might take only after ensuring the device is completely unplugged. Checking the fuse while the unit is still plugged in exposes you to live AC mains.