Speech Emotion Recognition (SER) is a significant research field in human-computer interaction, but it has difficulties in properly capturing the hierarchical, temporal, and complex dynamics that are present in emotional speech. To solve these challenges, a novel deep learning architecture is introduced, namely, the Squeeze-and-Excitation Temporal-GRU-Residual Network (SE-TGRNet). This model presents a hybrid framework that combines the power of several paradigms of neural networks. The architecture first starts with a frontend of residual blocks coupled with Squeeze-and-Excitation (SE) modules to learn strong, channel-attentive local features from Mel-Frequency Cepstral Coefficients (MFCCs). A Temporal Convolutional Network (TCN) block is then used to learn long-range temporal dependencies in an efficient way. Next, a multi-layer Bidirectional Gated Recurrent Unit (BiGRU) network captures contextual relationships between feature sequences. This hierarchical architecture enables SE-TGRNet to be able to learn discriminative features across various temporal scales. Experimental results on benchmark datasets confirm that the proposed approach achieves state-of-the-art performance, validating the advantages of integrating residual, attention, temporal convolutional, and recurrent components for SER.