I’ve run into a similar problem after a breaker got tripped in my house. I replaced the power supply and conducted the LED test. (NOTE: on my model there are 3 LEDs just to the right of the RAM slots on the logic board.) Everything seems to check out according to the LED indicators however the system will start up, chime and everything, run for maybe 15-20 seconds and then shut off. I’ve done both the SMC and PMU resets but still have the same issue.
Any help on narrowing down what the issue is would be greatly appreciated.