Mac Pro Late 2013 won't start

Another way to effect SMC Reset is to disconnect AC power cord, press and hold the power-on button for a quarter minute, restore AC power cord, wait a quarter minute, then attempt to power on.

Because there is an 'always-on' power supply inside Mac Pro, you may experience minor arcing when you restore the power cord. This is normal, not a defect.

One other usual simple fix was to check the Coin Cell battery for at least the minimum 3 volts. However on these Macs, getting access to the the coin cell battery is a exceptionally complicated.

Sounds like a blown capacitor, or Ground Loop. which would not show n any HW test.

But in the past it has been a bad power button on some models.

https://www.ifixit.com/Answers/View/541281/2013+Mac+Pro+No+Power

https://www.ifixit.com/Answers/View/305285/New+Mac+Pro+suddenly+doesn't+turn+on

Well, that is the exact symptom of a charge bleeding down after a bit,& blown caps a a major cause of that, Ground Loops another cause.

On Pram, that is what tells the Mac how & where to boot from.

Sounds like a blown capacitor, or Ground Loop. but have you tried it with nothing else plugged into it?

Those are also the classic symptoms of dead coin-cell battery, for Macs as old as the PowerMac G3.

Thanks, I know about the older Macs, but haven't actually seen it prevent booting in later Macs. :)