The first symptom of a bad water pump is having the check engine light on. You won’t get a code specifically for a bad water pump, since most water pumps are mechanical. However, you might retrieve a P0217, indicating that the engine is overheating (engine overheat condition). This code could pop up if the ECT (engine coolant temperature sensor) senses the engine coolant temperature getting too hot.
Ensure you can access your car's diagnostic codes by acquiring an OBD2 scanner here.
You can still have a faulty water pump with no check engine light so let's move on to the next symptom.