Speech Emotion Recognition (SER) presents a significant yet persistent challenge in human-computer interaction. While deep learning has advanced spoken language processing, achieving high performance on limited datasets remains a critical hurdle. This paper confronts this issue by developing and evaluating a suite of machine learning models, including Support Vector Machines (SVMs), Long Short-Term Memory networks (LSTMs), and Convolutional Neural Networks (CNNs), for automated emotion classification in human speech. We demonstrate that by strategically employing transfer learning and innovative data augmentation techniques, our models can achieve impressive performance despite the constraints of a relatively small dataset. Our most effective model, a ResNet34 architecture, establishes a new performance benchmark on the combined RAVDESS and SAVEE datasets, attaining an accuracy of 66.7% and an F1 score of 0.631. These results underscore the substantial benefits of leveraging pre-trained models and data augmentation to overcome data scarcity, thereby paving the way for more robust and generalizable SER systems.