We propose a novel stochastic radio resource allocation strategy that achieves long-term fairness considering backhaul and air-interface capacity limitations. The base station is considered to be only powered with a finite battery that is recharged by an energy harvesting source. Such energy harvesting is also taken into account in the proposed resource allocation strategy. This technical scenario can be found in remote rural areas where the backhaul connection is very limited and the base stations are fed with solar panels of reduced size. Our results show that the proposed scheme achieves higher fairness among the users and, in some cases, a higher sum-rate compared with the well-known proportional fair scheduler.