How does a microwave door interlock work and is a DIY repair feasible?
This particular model has three microswitches to detect the door being fully closed.


If any one of them are loose or defective, it would cause the symptoms you experience.  Each switch is pricey at $30 from GE or $23 from Amazon but there are many low priced sources (see comments below), so I would open up the appliance and have a look to see if a wire has come loose, or a switch is no longer seated properly.  With it open, you should also be able to trigger the switch and see if it sounds like it is working correctly.  With this type of switch, listening to it can successfully diagnose them 90% of the time.

If all the switches seems mechanically okay, then bust out a DMM and use the ohmmeter to see which one is not remaining closed when toggled.