Umbilical Cord Blood for Stem Cell Transplantation in Treating Young Patients With Malignant or Nonmalignant Diseases

DISEASE CHARACTERISTICS: * Diagnosis of malignant or non-malignant disease, including but not limited to any of the following: * Acute myeloid leukemia or acute lymphoblastic leukemia (ALL) with resistant disease beyond first clinical remission (CR) * ALL in first CR at high-risk because of 1 of the following factors: * Hypoploidy * Pseudodiploidy with translocations t(9;22), t(4;11), or t(8;14) * Elevated WBC at diagnosis as follows: * \> 100,000/mm\^3 for patients 6-12 months of age * \> 50,000/mm\^3 for patients 10-20 years of age * \> 20,000/mm\^3 for patients 21 years of age * Burkitt's lymphoma/leukemia * Chronic myelogenous leukemia in first chronic phase or beyond * Juvenile myelomonocytic leukemia * Advanced stage or relapsed lymphoma * Advanced stage or relapsed solid tumors, including any of the following: * Neuroblastoma * Ewing's sarcoma * Rhabdomyosarcoma * Myelodysplastic syndromes, excluding patients with grade 3 or 4 myelofibrosis * Familial erythrophagocytic histiocytosis * Histiocytosis unresponsive to medical management * Inborn errors of metabolism * Langerhans cell histiocytosis unresponsive to medical management * Immune deficiencies, including: * Severe combined immune deficiency * Wiskott-Aldrich * Hemoglobinopathies, including sickle cell disease and thalassemia * Severe aplastic anemia * Fanconi's anemia * Metabolic storage diseases * Unrelated cord blood don…