OK,
Power down the PSU by removing the short between Green and Black.
Flip the switch at the back.
Measure the resistance between the two connectors of the power switch on the case. It gets connected to the motherboard with a connector that is probably labeled "Power".
So, you need to change the setting on your meter to read resistance and connect each one of its cables to one of the two connectors.
We are doing this measurement on a bare case with no PSU.
The resistance should be very high. While you are measuring the resistance, if you press the power switch on the case, the resistance should drop to 0. it may read something between 0 to 1 Ohm.
I will be back in about an hour.
If the power switch measures OK, you should place the motherboard on a non-conductive surface like its antistatic bag on a table and connect the CPU with the cooler, RAM, graphics card, PSU keyboard and mouse only. Nothing else. You also need a speaker.
Connect the monitor and power up and listen for beeps or diagnostic messages.
The fan should not spin until you short the two power pins on the motherboard where you connect the power connector from the case.