When diagnosing a faulty starter motor in a Hyundai Tiburon, start by checking the battery voltage to ensure it is sufficient. If the battery is charged, but the starter motor does not engage, tap it lightly with a rubber mallet while attempting to start the engine. If this works, it is an indication of a worn or faulty starter motor. However, it is recommended to consult the vehicle's owner's manual or seek professional assistance for a thorough diagnosis and proper replacement.