Privacy leakage and Byzantine agents are two critical issues that bring great challenges to the intelligent decision-making process of multi-agent systems (MASs). Considering the presence of these two issues, this paper targets the resolution of a class of nonconvex optimization problems under the Polyak-{\L}ojasiewicz (P-{\L}) condition. To address this problem, we mask the local gradients with Gaussian noises and adopt a resilient aggregation method self-centered clipping (SCC) to design a differentially private (DP) decentralized Byzantine-resilient algorithm, namely DP-SCC-PL, which simultaneously achieves differential privacy and Byzantine resilience. Theoretical analysis demonstrates that DP-SCC-PL achieves the consensus among all reliable agents with a decaying step-size and sublinear (inexact) convergence with a constant step-size, where the asymptotic convergence error is characterized in both cases. It has also been proved that if there are no privacy issues and Byzantine agents, then the asymptotic exact convergence can be recovered when adopting a well-designed decaying step-size. Numerical experiments verify the differential privacy, resilience, and effectiveness of DP-SCC-PL via tackling a nonconvex optimization problem satisfying the P-{\L} condition under various Byzantine attacks.