power button does not do anything

Does it make a difference if the power cord is attached or not?

You could try resetting the SMC: with MBP plugged in, press and hold CMD-OPT-SHIFT and then the power button ( I generally hold them for a ten count). You should see the charge light on the pwr adapter flip color (from amber to green or vice versa) after you release all. Then try powering on.