Transformers are vital elements in electrical networks, but they are prone to various faults throughout their service life. Among these, a winding short-circuit fault is of particular concern to researchers, as it is a crucial and vulnerable component of the transformers. Therefore, if this fault is not addressed at an early stage, it can increase costs for users and affect industrial processes as well as other electrical machines. In recent years, the analysis of vibration signals has emerged as one of the most promising solutions for detecting faults in transformers. Nonetheless, it is not a straightforward process because of the nonstationary properties of the vibration signals and their high-level noise, as well as their different features when the transformer operates under different conditions. Based on the previously mentioned points, the motivation of this work is to contribute a methodology that can detect different severities of short-circuited turns (SCTs) in transformers in both transient and steady-state operating regimes using vibration signals. The proposed approach consists of a wavelet-based denoising stage, a short-time Fourier transform (STFT)-based analysis stage for the transient state, a Fourier transform (FT)-based analysis stage for the steady-state, the application of two fault indicators, i.e., the energy index and the total harmonic distortion index, and two neural networks for automatic diagnosis. To evaluate the effectiveness of the proposed methodology, a modified transformer is used to experimentally reproduce different levels of SCTs, i.e., 0-healthy, 5, 10, 15, 20, 25, and 30 SCTs, in a controlled way. The obtained results show that the proposed approach can detect the fault condition, starting from an initial stage for consolidation and a severe stage to accurately assess the fault severity, achieving accuracy values of 90%.