Cardiovascular diseases represent a leading cause of mortality worldwide, necessitating accurate and early diagnosis for improved patient outcomes. Current diagnostic approaches for cardiac abnormalities often present challenges in clinical settings due to their complexity, cost, or limited accessibility. This study develops and evaluates novel deep learning architectures that offer fast, accurate, and cost-effective methods for automatic diagnosis of cardiac diseases, focusing specifically on addressing the critical challenge of limited labeled datasets in medical contexts. We propose two innovative methodologies: first, a Multi-Branch Deep Convolutional Neural Network (MBDCN) that emulates human auditory processing by utilizing diverse convolutional filter sizes and power spectrum input for enhanced feature extraction; second, a Long Short-Term Memory-Convolutional Neural (LSCN) model that integrates LSTM blocks with MBDCN to improve time-domain feature extraction. The synergistic integration of multiple parallel convolutional branches with LSTM units enables superior performance in heart sound analysis. Experimental validation demonstrates that LSCN achieves multiclass classification accuracy of 89.65% and binary classification accuracy of 93.93%, significantly outperforming state-of-the-art techniques and traditional feature extraction methods such as Mel Frequency Cepstral Coefficients (MFCC) and wavelet transforms. A comprehensive 5-fold cross-validation confirms the robustness of our approach across varying data partitions. These findings establish the efficacy of our proposed architectures for automated heart sound analysis, offering clinically viable and computationally efficient solutions for early detection of cardiovascular diseases in diverse healthcare environments.