Hmmm. Thread seems to be missing some earlier posts, so we'll start "from scratch".
What you describe appears to be brief attempt at start-up followed immediately by a complete shut-down. I can think of four things that can cause such.
1. On virtually all mobos the CPU_FAN header does THREE jobs. It provides power to the CPU cooler, it adjusts that cooler device's speed, and it monitors that device's speed signal for NO signal (or in some cases, a speed too low) that indicates failure. Failure detection means that the mobo will shut down the system completely right away, without waiting for the temperature sensor inside the CPU chip to show high temps. This is to prevent very rapid heating of the expensive CPU leading to permanent damage from NO cooling. So, check whatever device you have for the CPU cooling (fan and heatsink, or pump of a AIO liquid-cooled system). WHERE is that plugged in? IF it is NOT in the CPU_FAN header, move it to there. IF it is plugged in there, UNplug it, then plug back in again. Repeat a few times. Then CHECK that it is secure AND that you did not disturb any other things during this time. This action may "scrub" any dirty surface on the contacts in the connector so it makes good contact again. Now try to start up. Does that particular fan start even briefly? Or does it do nothing? Or (hopefully) it runs properly.
2. On most systems there is a multi-contact cable from the PSU directly to a socket on the mobo very near the CPU ship that is power for that chip alone. This is in addition to the largest PSU output cable going to the mobo. Without that connected securely it cannot start up.
3. In making your changes (replacing the PSU plus ???) did you remove the mobo from the case? Do you know for sure that the system worked properly BEFORE the PSU replacement? I'm thinking about mis-location of the stand-offs under the mobo that hold the mobo away from the backing plate of the case. A stand-off in the wrong spot can cause a short circuit from a mobo trace on the bottom side to the case. But if you never had that problem before, it is possible but not very likely that this is your problem. If you need more info on this, post back here.
4. It is possible your new PSU is faulty. Can you replace it temporarily with a known-good PSU to check? I once had a PSU that failed slowly over a period of many months. A main symptom was that the system would crash completely and not re-start until I disconnected from the wall outlet for 15 min, then plugged back it. It would start and run for a while, then fail again.