DIAGNOSIS The LED is a simple circuit, so when it dies, it's usually one of three things: a burned-out LED bulb, a broken wire leading to it, or a failure in the small circuit board that powers it.
FIX First, check for the obvious. Look closely at the clear plastic window covering the LED. Is it caked with sawdust or paint? Clean it off. Sometimes the light is working but completely obscured. Next, operate the drill in a dark room. You might see a very faint glow if the LED is partially failed.
IF THAT DIDN'T WORK If it's truly dead, the LED unit itself is likely the culprit. It's a single, small module that's replaceable if you open the drill. The part usually includes the LED and the little plastic housing. The wiring is typically just two solder points.
HEADS UP The work light circuit is separate from the motor circuit, so the drill will keep working fine without it. When you open the drill to replace it, be careful not to pinch or cut the thin wires that run to the LED—they're easy to miss.