MacBook Pro 15 Mid 2010 Logic Board (power button) Problem

I've little problem of motherboard in my Mac. The only symptom of damage is an error with the power button (pressing it cuts the power until the battery is removed).

I also noticed a curiosity that may help in the diagnosis. It's hard to explain, but I'll try.

If I turn off the mac, I have to do a battery reset (disconnect and connect after 5 or more seconds) and connect magsafe. Mac starts (does what it should) fans starts to spin etc.

And now the most interesting. If I press the power button BEFORE the screen and the startup sound appear, the Mac shuts down and in a short while it starts up again, I can do it endlessly. However, if I press the power button AFTER the screen and sound appear, I have to repeat the operation with the battery.

Also, if I'm doing a "BEFORE" thing and holding the power button, nothing happens until I release it.

I can solder and I have tools for that. In my life, I have repaired some audio things (pcb too) and thought to take the risk of replacing the parts responsible for the power supply.

I risk not much, because the motherboard has to be replaced anyway, so it's worth trying.

Maybe somebody could help me where to start looking for damaged parts, or there is someone on the forum who has dealt with a similar case?