It's a common problem I run into. Either an overtaxed PSU or motherboard standoffs are shorting the backside. Mind you it can work for years and then this.
I don't see PSU make, model of the new unit and the symptoms are correct for the old standoff issue. We pull the machine out of the case to test it with bare min parts and work our way back to a full PC. Checking standoffs again for any extras.
I built a comp. about 3-4 years ago (specs: https://pcpartpicker.com/list/yVvcnQ) that I never had performance issues from. A few months ago, the computer had turned off from sleep mode and would not turn on. No lights or fans. I moved it to different outlets and tried different cords and eventually it came back on with the original outlet and cord. Every few weeks since it would happen again and there was no consistent way for me to get it back on- just randomly will after I move it around and plug/unplug things. I got a PSU tester and it read fine.
Recently while running a game (again never have had issues with performance while gaming), it completely shut off and would not start. I tested the PSU and it didn't read as good, so I bought a new PSU. The new PSU tested good so I plugged it in. When trying to turn the computer on with the new PSU, fans and LEDs will flicker, but then stop. I took the new PSU out and went back to the old PSU and was able to get the computer started. Started up a game and the computer died again. I repeated the process of trying both PSUs and got the same result of the new one not starting it up, but the old one starting. I'm posting this while on the computer, but I'm afraid if I open any game or turn the computer off, I will have the issue again.
Does anyone have any thoughts about my issue? I'm thinking replacing my motherboard will work, but the inconsistencies with these PSUs is making me question that. Thanks for any help!