Modern wind turbines depend on their blade pitch systems for start-ups, shutdowns, and power control. Pitch system failures have, therefore, a considerable impact on their operation and integrity. Hydraulic pitch systems are very common, due to their flexibility, maintainability, and cost; hence, the relevance of diagnostic algorithms specifically targeted at them. We propose one such algorithm based on sensor data available to the vast majority of turbine controllers, which we process to fit a model of the hydraulic pitch system to obtain significant indicators of the presence of the critical failure modes. This algorithm differs from state-of-the-art, model-based algorithms in that it does not numerically time-integrate the model equations in parallel with the physical turbine, which is demanding in terms of in situ computation (or, alternatively, data transmission) and is highly susceptible to drift. Our algorithm requires only a modest amount of local sensor data processing, which can be asynchronous and intermittent, to produce negligible quantities of data to be transmitted for remote storage and analysis. In order to validate our algorithm, we use synthetic data generated with state-of-the-art aeroelastic and hydraulic simulation software. The results suggest that a diagnosis of the critical wind turbine hydraulic pitch system failure modes based on our algorithm is viable.