Diagnosis
This is either a second failed bulb or a problem with the light socket or its wiring. A faulty door switch can also interrupt the light circuit.
How to Fix It
Confirm you used a 40W appliance bulb with an E26 base. Ensure it is screwed in tightly. Test the old bulb and the new bulb in a known-working lamp socket. If both bulbs are good, check the light socket for charring or a loose center contact tab.
If That Didn't Work
The light circuit is controlled by the main control board. A failed relay on the board will not send power to the socket. The door switch must also be engaged for the light to operate. Test the door switches.
Heads Up
Do not use a bulb with a higher wattage than 40W. Over-wattage bulbs generate excess heat that can damage the socket and wiring, leading to this exact failure.