Barstow is an unincorporated community in Rock Island County, Illinois, United States. Barstow is east of East Moline and Silvis. Barstow is located on a wye that connects track owned by the BNSF Railway, including the Barstow Subdivision. These tracks were previously owned by the Chicago, Burlington and Quincy Railroad, and a station once exis…Barstow is an unincorporated community in Rock Island County, Illinois, United States. Barstow is east of East Moline and Silvis. Barstow is located on a wye that connects track owned by the BNSF Railway, including the Barstow Subdivision. These tracks were previously owned by the Chicago, Burlington and Quincy Railroad, and a station once existed within the wye.