Conjugate gradient (CG) methods are considered among the most efficient methods for solving optimization problems thanks to their straightforward iterative process and low memory requirements. In the present work, we propose a combined CG method to address large-scale problems, with a particular application to training artificial neural networks (ANNs) for early breast cancer prediction and electrocardiogram (ECG) classification. Under the strong Wolfe line search conditions, the global convergence was demonstrated under mild assumptions and the generated descent direction and the convergence features of the suggested approach are examined. The proposed approach was successfully applied to train neural networks for early breast cancer prediction, achieving an accuracy of 98.24%, with precision, recall, and F1-score values of 0.99, 0.97, and 0.98, respectively. It also reduces the final mean squared error by over 52% and exhibited faster convergence with smoother training dynamics. Furthermore, on the ECG classification dataset, the proposed hybrid Dai-Liao (hDL ${}^{+}$) achieves an accuracy of 80.45%, demonstrating strong generalization performance across different medical diagnostic applications. Comparisons with recent CG methods on a set of test problems from the CUTE library confirmed the robustness and efficiency of the proposed method.