Ok that was easy enough, you need a new door latch assembly the 3 beeps is a fault code for the door latch assembly. Dont worry about the cycling thermaststat its suppose to sound like that.
Ok i fully understand, but you still need a new door latch assembly, this is the only way that you are going to fix this like i mentioned earlier them 3 beeps is a fault code for the door latch.
Electrically you would test it with a multi-meter. It should have no resistance when closed and infinite resistance when off.
Please post the model number