Existing data-driven control methods generally do not address False Data Injection (FDI) and Denial-of-Service (DoS) attacks simultaneously. This letter introduces a distributed data-driven attack-resilient consensus problem under both FDI and DoS attacks and proposes a data-driven consensus control framework, consisting of a group of comprehensive attack-resilient observers. The proposed group of observers is designed to estimate FDI attacks, external disturbances, and lumped disturbances, combined with a DoS attack compensation mechanism. A rigorous stability analysis of the approach is provided to ensure the boundedness of the distributed neighborhood estimation consensus error. The effectiveness of the approach is validated through numerical examples involving both leaderless consensus and leader-follower consensus, demonstrating significantly improved resilient performance compared to existing data-driven control approaches.