This paper provides a unified framework to deal with the challenges arising in dense cloud radio access networks (C-RAN), which include huge power consumption, limited fronthaul capacity, heavy computational complexity, unavailability of full channel state information (CSI), and so on. Specifically, we aim to jointly optimize the remote radio head (RRH) selection, user equipment (UE)-RRH associations and beam-vectors to minimize the total network power consumption (NPC) for dense multi-channel downlink C-RAN with incomplete CSI subject to per-RRH power constraints, each UE's total rate requirement, and fronthaul link capacity constraints. This optimization problem is NP-hard. In addition, due to the incomplete CSI, the exact expression of UEs' rate expression is intractable. We first conservatively replace UEs' rate expression with its lower bound. Then, based on the successive convex approximation technique and the relationship between the data rate and the mean square error, we propose a single-layer iterative algorithm to solve the NPC minimization problem with convergence guarantee. In each iteration of the algorithm, the Lagrange dual decomposition method is used to derive the structure of the optimal beam-vectors, which facilitates the parallel computations at the baseband unit pool. Furthermore, a bisection UE selection algorithm is proposed to guarantee the feasibility of the problem. Simulation results show the benefits of the proposed algorithms and the fact that a limited amount of CSI is sufficient to achieve performance close to that obtained when perfect CSI is possessed.