In this paper, the effects of energy harvesting (EH) on an automatic repeat request based cooperative communication network comprised of a source, a relay, and two destination nodes, are investigated in Rayleigh fading channels. The energy of the decode-and-forward relay is provided by EH throughout the radio frequency signal from the source. In the proposed transmission protocol, the source transmits a data packet to the relay and two destination nodes by direct links. If the transmission is successful at both destination nodes, these nodes reply by an acknowledgement (ACK) signal to the source and the relay. Otherwise, there are two alternatives: If the relay has received this data packet successfully and replied by an ACK signal, then it cooperates and transmits the data packet for a second time to two destination nodes. If the relay has failed and replied by a non-acknowledgement signal, the source in this case retransmits this packet to the destination nodes by direct links. First, a broadcast channel is considered where the source transmits the same data packet to the relay and destination nodes. Second, the non-orthogonal multiple access technique is applied to the same network where different packets are sent to each destination node by means of superposition coding. In both cases, the system throughputs are obtained from the derived closed-form expressions for the outage probabilities based on the Markov chain model. All theoretical results are supported by computer simulation results.