I had the same problem with my MAC machine and tried the all above troubleshooting but no vain, I replaced the PS but problem was same,
finally I though to open the power switch connectivity. Unplug the power switch cable tried to turn the system and plug back the power cable again. Actual problem found in power switch, its dont pull back properly and switch connectivity force the machine to shutdown. you should move switch right left and updown and have light finger touch to turn on the System. Replace it with new one if your power switch hv repeated issues. Thanks
Muhammad Shehzad, PK