Engagement detection in online learning environments is vital for improving student outcomes and personalizing instruction. We present ViBED-Net (Video-Based Engagement Detection Network), a novel deep learning framework designed to assess student engagement from video data using a dual-stream architecture. ViBED-Net captures both facial expressions and full-scene context by processing facial crops and entire video frames through EfficientNetV2 for spatial feature extraction. These features are then analyzed over time using two temporal modeling strategies: Long Short-Term Memory (LSTM) networks and Transformer encoders. Our model is evaluated on the DAiSEE dataset, a large-scale benchmark for affective state recognition in e-learning. To enhance performance on underrepresented engagement classes, we apply targeted data augmentation techniques. Among the tested variants, ViBED-Net with LSTM achieves 73.43\% accuracy, outperforming existing state-of-the-art approaches. ViBED-Net demonstrates that combining face-aware and scene-aware spatiotemporal cues significantly improves engagement detection accuracy. Its modular design allows flexibility for application across education, user experience research, and content personalization. This work advances video-based affective computing by offering a scalable, high-performing solution for real-world engagement analysis. The source code for this project is available on https://github.com/prateek-gothwal/ViBED-Net .