In this paper, we aim to minimize the network power consumption (NPC) in a downlink cloud radio access network. Not only the powers consumed at remote radio heads and fronthaul links for transmission, but also the power consumed at the baseband unit pool for computation is considered. We formulate a joint NPC minimization problem as a mixed timescale issue which can be regarded as a combination of two power minimization problems for computation and transmission, where the former is a slow timescale issue since task scheduling and computation resource allocation are usually executed in a large time space whereas the latter is a fast timescale issue due to the dependence on small-scale fading. To deal with timescale challenge, we introduce approximate results of the joint NPC minimization problem according to large system analysis and turn it into a slow timescale issue because the approximations are only dependent on statistical channel information. We propose an iterative coordinate descent algorithm based on branch-and-bound algorithm to find solutions to the joint NPC minimization problem. Numerical results show that the NPC decreases as the delay constraint increases but increases if the execution efficiency or computing capability of servers is degraded.