A burner that clicks steadily but never lights is almost always the igniter itself — either worn out from years of sparking or fouled by debris sitting in the burner port right where the spark needs to jump. Because the spark only has to cross a gap of a few millimeters, a thin film of grease or a damp crumb left behind after a boil-over is enough to stop it — and that film accumulates gradually rather than all at once.
Before calling it in, a careful visual check of the burner cap and port for visible debris is worth doing (with the range off and cooled), but if cleaning the visible area doesn’t resolve it, the igniter or its spark module is the more likely cause — a targeted, generally affordable repair rather than anything involving the range’s main control system.