Axial piston pumps are crucial components in fluid power systems, where reliable fault diagnosis is essential for ensuring operational safety and efficiency. Traditional data-driven methods require extensive labeled fault data, which is often impractical to obtain, while model-based approaches suffer from parameter uncertainties. This paper proposes a digital twin (DT)-driven zero-shot fault diagnosis framework utilizing fluid-borne noise (FBN) signals. The framework calibrates a high-fidelity DT model using only healthy-state data, generates synthetic fault signals for training deep learning classifiers, and employs a physics-informed neural network (PINN) as a virtual sensor for flow ripple estimation. Gradient-weighted class activation mapping (Grad-CAM) is integrated to visualize the decision-making process of neural networks, revealing that large kernels matching the subsequence length in time-domain inputs and small kernels in time-frequency domain inputs enable higher diagnostic accuracy by focusing on physically meaningful features. Experimental validations demonstrate that training on signals from the calibrated DT model yields diagnostic accuracies exceeding 95\% on real-world benchmarks, while uncalibrated models result in significantly lower performance, highlighting the framework's effectiveness in data-scarce scenarios.