OBJECTIVES: I. Estimate the maximum tolerated dose of carboplatin that can be given in combination with cyclophosphamide (CTX) and etoposide following high dose CTX, doxorubicin, and vincristine in patients with newly diagnosed stage IV neuroblastoma. II. Determine the hematologic and nonhematologic toxic effects of this regimen in this patient population. III. Determine the change in neuroblastoma tumor cell content in peripheral blood stem cells (PBSC) collected following chemotherapy. IV. Assess the feasibility of repetitive collection, storage, and infusion of PBSC with multicycle high-dose chemotherapy in pediatric patients. V. Assess hematopoietic recovery following PBSC infusion as well as the CD34 content and CFU-GM yield of the PBSC products. VI. Assess the response rate and disease-free survival in the context of a phase I pilot study. VII. Determine the feasibility of administering twice-daily radiotherapy fractions to post-chemotherapy residual tumor volumes in neuroblastoma patients.