Diagnosis
This is almost certainly a failed door switch or a burnt-out bulb. The switch is a small plastic plunger near the top of the door frame that gets pressed in when the door closes.
How to Fix It
First, check the obvious. 1) Unplug the unit for safety. 2) Open the door and locate the small plastic button/plunger at the top of the door opening. Press it in and out with your finger a bunch of times—it might just be stuck. 3) While you're there, look at the small light bulb cover. If it's accessible, try gently turning the bulb (if it's the screw-in type) to ensure it's seated. Plug it back in and test. If that doesn't work, the bulb is likely dead.
If That Didn't Work
If fiddling with the switch or bulb doesn't help, the switch itself may have failed electrically. You'd need to access it from behind the interior liner, which is a more involved repair to test and replace the micro-switch.
Heads Up
If you replace the bulb, you must use the exact same type and wattage (usually a small, low-wattage incandescent or specific LED). Using a higher-wattage bulb can generate too much heat and damage the plastic housing or wiring.