Power to microwave light inside work but display does not.

Usually three different micro-switches work off of your door latch. Usual setup: 1 for light, 1 for safety on low-voltage side of your power supply (where your problem probably is), and one for the high-voltage side. Remove your cover (unplug unit first please), check the physical operation of all visible micro-switches as you open and close the door. If they all are changing function as they should, use an ohm-meter to check each switch for continuity. Remove one lead off each switch so the meter isn’t reading into the power supply. From what you describe, 9 times out of ten the problem will be in the microswitches. Having to reposition one or more switches is not unheard of as the microwave ages. Good luck… And never work on a microwave with the cord plugged in. (That’s why I look like 103 instead of 43!)