Hi ,
Don’t know your laptop but I’m wondering if there is a problem with the Power switch on the laptop.
Can you use an Ohmmeter and test it for continuity when the button is pressed? Disconnect the switch from the motherboard before you try this.
Here’s a link to a video that shows how to dis-assemble the laptop so that access to the Power switch pcb is possible (although given that you have replaced the motherboard you probably know how to dis-assemble it already).
If the power switch is faulty here are the part numbers for the Power switch pcb for the various Asus N76V models
N76VM and N76VZ : 90R-NALPS1000Y
N76VJ :90NB0040-R10030
N76VB : 90NB0130-R10020
if you search online using the part number only there are results for suppliers of the part. Not all the part numbers were getting results for suppliers.
If you are in Europe, try this link (change the model number to suit - box #4), select “Sub board” category and find the Power switch pcb