Diagnosis
The door switch actuator is broken, or the bulb is burnt out. The switch tells the light to turn on.
How to Fix It
First, replace the bulb. It's a standard 10-watt appliance bulb (part # 310726). If that doesn't work, check the door switch plunger. Open the door. The small plastic actuator on the door frame should press the switch firmly. If it's broken, replace the actuator.
If That Didn't Work
The door switch itself (part # 310241A) may be faulty. Unplug dryer. Test the switch for continuity when the plunger is pressed. No continuity means a bad switch.
Heads Up
Unplug the dryer before changing the bulb or checking the switch. The light circuit is not always isolated when the dryer is off.