A distributed or multi-channel system consisting of multiple sensors is considered. At each sensor a sequence of observations is taken, and at each time step, a summary of available information is sent to a central decision maker, called the fusion center. At some point of time, the distribution of observations at an unknown subset of the sensor nodes changes. The objective is to detect this change as quickly as possible, subject to constraints on the false alarm rate, the cost of observations taken at the sensors and the cost of communication between the sensors and the fusion center. Minimax formulations are proposed for this problem. An algorithm called DE-Censor-Sum is proposed, and is shown to be asymptotically optimal for the proposed formulations, for each possible post-change scenario, as the false alarm rate goes to zero. It is also shown, via numerical studies, that the DE-Censor-Sum algorithm performs significantly better than the approach of fractional sampling, where the cost constraints are met based on the outcome of a sequence of biased coin tosses, independent of the observation process.