Why does my power button not react with charger in?

My problem is that when I press the power button nothing happens and it does not boot up. It neither does an SMC reset. It's like it doesn't function. HOWEVER, when I disconnect the magsafe (which lights up properly amber and green) it DOES function (it turns on ok). However once in OSX it DOES NOT function and does not switch off when you hold it down. I replaced the charger still the same problem. I replaced the magsafe board itself - still the same problem. I changed the flex cable connecting magsafe to logic board - still the same problem, replaced the fan - still the same problem. It does not work when I plug the charger in (when its amber) though you can put it back inonce its on and it charges the battery as normal. It runs off the battery obviously fine. I replaced the keyboard too - in case it was the power button, but still with a brand new keyboard its still the same problem. I ran diagnostics and it mentions something about the EXHAST which I think is the fan but nothing helps! ANY SUGGESTIONS?? I have tried reintalling OSX and have tried everything else! Thanks!

I have now replaced the motherboard a second time, with again a different one. Still the same problem. What could it be as I replaced literally everything!