Why will my car not start even though the lights work?

Working lights prove there is some charge, not that there is enough. Lights draw a very small current compared with a starter motor, which needs several hundred amps. A battery too weak to crank can comfortably light the dashboard, which is why this symptom misleads people into ruling out the battery.

The sound when you turn the key narrows it considerably.

A single loud click, or a rapid clicking, almost always means insufficient current reaching the starter. Usually that is a weak battery, but corroded or loose battery terminals produce the identical symptom with a perfectly good battery. Terminals are worth inspecting and cleaning first because it costs nothing; a white or blue-green deposit is the giveaway.

No sound at all points elsewhere: the ignition switch, a starter relay, an immobiliser not recognising the key, or on an automatic a neutral safety switch that does not think the car is in park. Trying to start in neutral rather than park is a quick test for that last one.

Cranking normally but not firing means the electrical side is fine and the engine is missing fuel, spark or compression. That is a different investigation entirely, and the fact that it cranks is genuinely useful information.

A grinding noise suggests the starter is engaging badly, which needs attention rather than repeated attempts.

One modern complication: many cars with automatic stop-start systems behave oddly when the battery is marginally weak, disabling features and sometimes refusing to start, because the system monitors battery condition. A battery that tests as merely acceptable can cause this, and replacing it resolves what appears to be an electronic fault.