I had this issue very recently and figured out how to fix this after lots and lots of reading, trial, error, and re-reading. I’ll walk you through what I did in the hope that someone else finds this useful.
For background, I am on a 2009 Mac Pro 4,1 flashed to 5,1. Single tray 6 Core, 32 GB RAM, RX580 GPU running 10.13 High Sierra.
Ok, so I had noticed that my computer had been randomly shutting itself off. The frequency of which was impossible to predict, so I began the google search to see if I could dig up an easy fix. Hint: Nothing is ever as easy as you think, I’ve found. After an entire afternoon of reading through what other folks did to fix this happening to them, I set out to try it and each test/fix failed. I then deduced that it must be the power supply, as the random shut downs seemed to indicate that it needed to be replaced.
I ordered a new PSU, which came in a couple of days and installed it. Tried to power on, no luck. No clicks, no lights, no nothing. I was a little disappointed as everything I had read to that point had shown me that this would fix it. I then hit google again in an effort to better define my search terms and see if I had missed something. One site said to change PRAM batter, another said to switch the RAM around in their sockets. None of this worked for me. Finally, I got ahold of the Apple Diagnostic PDF which the techs at Apple use to figure out problems. I suggest anyone having this issue download a copy and keep it on file both on your mobile device and on your computer. There is a bit of nuance with it in that the guide won’t tell you what to do should something fail a specific test, at least not obviously. That being said, with a little abstract thought, reasoning, and google, anyone should be able to diagnose what’s wrong.
I followed the guide and when I found that my computer WOULD NOT turn on after jumping the solder spots, as instructed by the guide, I knew it had to be the logic board/backplane. If the power supply and LED test (on the upper left of the logic board as you look at it with the side cover removed) showed that the board was receiving standby power yet wouldn’t turn on, all indications pointed to a bad logic board. I promptly ordered one that was correct for my Mac Pro (remember, it’s a 4,1 flashed to 5,1 so I needed to be sure that I bought the right one, ensure you double check with sellers/stores before you haphazardly click buy so you don’t have to go through a return process or deal with fans that run at full blast 24/7). When it arrived, I installed it and then re-installed all the other components. I plugged in the power cord and, there it was. It started right up as if nothing had happened.
Following the guide will get you to this exact conclusion point I reached after trying two other methods that failed to fix the problem. Usually, motherboards either work or they don’t. The fact that mine would work sometimes had me leaning more towards a PSU, but this one turned out to be a backplane. If you are experiencing these same symptoms of random power offs, no clicks when you push the power button, and eventually no reaction whatsoever when you do push the power button, I’d bet my money on the backplane.
I hope this helps anyone experiencing this issue. My intent is for this to be a fast-track to help others so they don’t have to go through multiple levels of trial and error before fixing the issue, but I do know the value of finding the simple fixes when they exist. I’d always recommend you take the time to investigate and troubleshoot all avenues that could be causing your power issues, but this particular one was solved with a logic board.