Your problem is the Felpxcable from the POWER/EJECT Buttons board. Remove that Flex cable and examine it carefully! You will see the contacts are ****ed.
you can get a new one cheap on ebay. If the Contacts are only screwed on in the edges, you could cut them and use the cable to turn on and off your ps3 until your new cable comes.
I have repaired my Ps3 like this before. Its not the power supply! It is the cable!
Can you make a picture of your cable so I can see it ?
PS: My ps3 did not start without the board being plugged in... after i fixed the cable everything was fine again...
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