"The best way to check the PSU is to swap it with a known good PSU of similar capacity. Brand new, out of the box, untested does not count as a known good PSU. PSU's, like all components, can be DOA.
Next best thing is to get (or borrow) a digital multimeter and check the PSU.
Yellow wires should be 12 volts. Red wires: +5 volts, orange wires: +3.3 volts, blue wire : -12 volts, violet wire: 5 volts always on. Tolerances are +/- 5% except for the -12 volts which is +/- 10%.
The gray wire is really important. It should go from 0 to +5 volts when you turn the PSU on with the case switch. CPU needs this signal to boot.
You can turn on the PSU by completely disconnecting the PSU and using a paperclip or jumper wire to short the green wire to one of the neighboring black wires.
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This checks the PSU under no load conditions, so it is not completely reliable. But if it can not pass this, it is dead. Then repeat the checks with the PSU plugged into the computer to put a load on the PSU. You can carefully probe the pins from the back of the main power connector."