The sound of a MW running can tell you if the magnetron is on. If not, you put a cup of water in when it does this does it warm the water? If the magnetron is running, that is definitely not good. If just the fan and maybe the table is running, that is not proper but not dangerous.
Possible problem for either:
# a shorted switch
# the control board as that is what would switch off the system when the door is opened or the cancel button is pressed.