Hi,Welcome to Just Answer, My name isXXXXX will be helping you with your appliance issue today.
if all the other funtions work but it just wont start the
Primary/secondary micro switch is most likely the cause. there are 3 door switches and they are safety's if the switch fails it wont start. this is so the microwave wont run when the door is open, you need to check the switches, if your real confident in doing this I strongly advise calling a technician in to test the switches, microwaves a very dangerous to work on in this requires opening up the control panel to access the switches., This exposes you to extremely high voltages in the microwave cavity itself, microwaves can store a lethal amount of voltage in the high-voltage capacitor and can kill you if you hit the wrong wire while trying to test the switches, this is what the switch looks like,
these are two-way switches so the light can still come on when you open the door but that doesn't mean this switch is good, please be safe and call a technician if you're unsure how to do this, thanks and well wishes, Bryan