I found the final cause for this issue, short circuit on the board, it is very hard to find a shorted component.
I isolated all circuits by removing the solder bridges, around 7 or 8 PJPxxx in the schematics
b2f74_Compal_LA-9104P_VAW00_Inspiron_3521.pdf
that only learned me that the short did not go away, so it must be real close to the entry.
I singled out where the short then might be and started to remove capacitor PC105, PC106 , PC 104 bingo!!!!
The 4.7U_0805_25V6-K had shorted because of the ESD!
I replaced it with some 1206 cased tantalum cap I had around, had to resolder all PJPxxx joints and the AO4409 that had died because of the short.
Connected PSU and no more switching off
Put all back together and voila!!! It worked again!! Hurray!
Here the same issue and a picture
http/www.badcaps.net/forum/showpost.php?p=578437&postcount=50
Some months ago I searched and found a similar case where this cap was shorted, I guess a common cause for these kind of ESD shorts.
I have some AO4409 and AO4407 left for repair, ping me if you have a need in NL or EU.