With the growing capacity of distributed renewable energy resources (RERs) integrated into distribution grids, the power flow distribution becomes more complex. Traditional fault diagnosis solutions are proving inadequate for the demands of the evolving distribution network, thereby diminishing the reliability and sensitivity of the protection system. To address this challenge, this paper introduces an innovative fault diagnosis approach for distribution networks incorporating RERs, leveraging signal processing techniques and machine learning algorithms. Initially, effective features are obtained from the measured current signals by the Hilbert-Huang transform (HHT). Subsequently, these fault features serve as inputs for training feed-forward neural networks to build fault diagnosis models (including detection, classification, and segment identification). Simulation tests are conducted on a 13-node distribution network with three different types of RERs. Simulation results show that the method can accurately diagnose distribution network faults, and is robust to fault inception angle variations, transition resistance, and noise interference.