This phase I/II partially randomized trial studies the side effects and best dose of veliparib when given together with radiation therapy, carboplatin, and paclitaxel and to see how well it works in treating patients with stage III non-small cell lung cancer that cannot be removed by surgery. Veliparib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Radiation therapy uses high energy x-rays to kill tumor cells and shrink tumors. Drugs used in chemotherapy, such as carboplatin and paclitaxel, work in different ways to stop the growth of tumor cells either by killing the cells, by stopping them from dividing, or by stopping them from spreading. It is not yet known whether radiation therapy, carboplatin, and paclitaxel are more effective with or without veliparib in treating non-small cell lung cancer.