A hydraulic system is disclosed for assisting starting of a machine having an engine. The hydraulic system may include a work tool, a pump driven by the engine to pressurize fluid, and an actuator configured to receive pressurized fluid from the pump and move the work tool. The hydraulic system may also include an accumulator configured to selectively receive pressurized fluid from the pump and from the actuator, an electric starter configured to start the engine, and a motor selectively supplied with fluid from the accumulator to assist the electric starter in starting the engine.