INDUCTION THERAPY: Patients undergo 3-dimensional conformal radiation therapy (3D-CRT) once daily (QD), 5 days a week, for 6 weeks. Patients also receive veliparib orally (PO) twice daily (BID) on days 1-43 and carboplatin intravenously (IV) over 30 minutes and paclitaxel IV over 1 hour on days 1, 8, 15, 22, 36, and 43 in the absence of disease progression or unacceptable toxicity. Patients without disease progression after completion of chemoradiotherapy undergo consolidation therapy.