Wireless Sensor Networks (WSN) are the backbone of essential monitoring applications, but their deployment in unfavourable conditions increases the risk to data integrity and system reliability. Traditional fault detection methods often struggle to effectively balance accuracy and energy consumption, and they may not fully leverage the complex spatio-temporal correlations inherent in WSN data. In this paper, we introduce HiFiNet, a novel hierarchical fault identification framework that addresses these challenges through a two-stage process. Firstly, edge classifiers with a Long Short-Term Memory (LSTM) stacked autoencoder perform temporal feature extraction and output initial fault class prediction for individual sensor nodes. Using these results, a Graph Attention Network (GAT) then aggregates information from neighboring nodes to refine the classification by integrating the topology context. Our method is able to produce more accurate predictions by capturing both local temporal patterns and network-wide spatial dependencies. To validate this approach, we constructed synthetic WSN datasets by introducing specific, predefined faults into the Intel Lab Dataset and NASA's MERRA-2 reanalysis data. Experimental results demonstrate that HiFiNet significantly outperforms existing methods in accuracy, F1-score, and precision, showcasing its robustness and effectiveness in identifying diverse fault types. Furthermore, the framework's design allows for a tunable trade-off between diagnostic performance and energy efficiency, making it adaptable to different operational requirements.