One of the commonest parts to fail in a desktop or tower system is the power supply, will will usually be a switch-mode power supply. You can test the voltages coming out of a power supply using a digital multi-meter while the supply is under load, but such readings don’t really mean very much. Even if a power supply is able to maintain voltages within required tolerances, it may nevertheless be incapable of supplying the required amount of current. Some power supplies have an LED on the back that glows green to show that everything is good. However, I’ve seen power supplies with green LEDs glowing that had effectively failed, so never take these ‘all is well’ indicators seriously. The simplest way of testing whether a power supply is the cause of a problem is to swap in a known-to-be-working replacement.