Umbilical Cord Blood Transplantation in Treating Patients With Hematologic Cancer or Nonmalignant Hematologic Disease

DISEASE CHARACTERISTICS: * One of the following diagnoses: * Acute myeloid leukemia (AML), with or without myelodysplastic syndromes * Not in first complete remission (CR)\* with translocations t(8;21) and inv (16) unless failure of first-line induction therapy * Not in first CR\* with translocations t(15;17) abnormality unless: * Failure of first-line induction therapy OR * Molecular evidence of persistent disease * Not in first CR with Down syndrome * Patients with third or greater medullary relapse or refractory disease (other than primary induction failures) receive busulfan/melphalan conditioning regimen NOTE: \* CR defined by no greater than 5% blasts in marrow * Acute lymphocytic leukemia (ALL) * Not in first CR OR * High-risk ALL in first CR, with high risk defined as one of the following: * Hypoploidy (no greater than 44 chromosomes) * Pseudodiploidy with translocations or molecular evidence of t(9;22), 11q23, or t(8;14) (except B-cell ALL) with or without MLL gene arrangement * Elevated WBC at presentation * Age 6-12 months: greater than 100,000/mm\^3 * Age 10-17 years: greater than 200,000/mm\^3 * Age 18: greater than 20,000/mm\^3 * Failed to achieve CR after 4 weeks of induction therapy * Patients with B-ALL must not be in first CR, must meet at least one of the high-risk criteria specified above, or must not meet any of the following criteria: * Translocation t(8;14) * Blasts have surface immunoglobulins * CD10 positive * Patients with third or greater medullary relapse or refractory disease (other than primary induction failures) receive busulfan/melphalan conditioning regimen * Chronic myelogenous leukemia, meeting criteria for 1 of the following: * Accelerated phase * Chronic phase if 1 year from diagnosis without a matched unrelated bone marrow donor AND unresponsive to or unable to tolerate interferon * Blast crisis, defined as greater than 30% promyelocytes plus blasts in bone marrow * Patients receive busulfan/melphalan conditioning regimen * Acute undifferentiated leukemia (AUL), infant leukemia, or biphenotypic leukemia * Patients with third or greater medullary relapse or refractory disease (other than primary induction failures) receive busulfan/melphalan conditioning regimen * Juvenile myelomonocytic leukemia meeting the following criteria: * No Philadelphia chromosome * Bone marrow blasts less than 30% * Peripheral blood monocytes greater than 1,000/mm\^3 * At least 2 of the following: * Peripheral blood spontaneous growth and/or sargramostim (GM-CSF) hypersensitivity * Increased hemoglobin F for age * Clonal abnormalities (e.g., monosomy 7 or RAS mutations) * Peripheral blood with myeloid precursors * WBC greater than 10,000/mm\^3 * Myelodysplastic syndromes defined by the following: * Refractory anemia (RA) * RA with ringed sideroblasts * RA with excess blasts (RAEB) * RAEB in transformation * Chronic myelomonocytic leukemia * Paroxysmal nocturnal hemoglobinuria * Hodgkin's lymphoma or non-Hodgkin's lymphoma beyond first CR or primary induction failures AND chemosensitive (greater than 50% reduction in tumor mass size) * Inborn error of metabolism including, but not limited to, Hurler's syndrome, adrenoleukodystrophy (ALD), Maroteaux-Lamy syndrome, globoid cell leukodystrophy, metachromatic leukodystrophy, fucosidosis, or mannosidosis * For ALD patients over age 5, IQ must be at least 80 * For all other patients over age 5, IQ must be at least 70 * For all patients age 5 and under, developmental quotient or clinical neurodevelopmental examination should demonstrate potential for stabilization at a level of functioning where continuous life support (e.g., mechanical ventilation) would not be predicted to be required in the year after transplantation * Combined immune deficiencies including, but not limited to: * Severe combined immunodeficiency (SCID) requiring cytoreduction * Wiskott-Aldrich syndrome * Leukocyte adhesion defect * Chediak-Higashi disease * X-linked lymphoproliferative disease * Adenosine deaminase deficiency * Purine nucleoside phosphorylase deficiency * X-linked SCID * Common variable immune deficiency * Nezelof's syndrome * Cartilage hair hypoplasia * No dyskeratosis congenita * No ALL, AML, AUL, or biphenotypic leukemia in third or higher medullary relapse or refractory disease other than primary induction failure * No primary myelofibrosis or myelofibrosis grade 3 or worse * No active CNS leukemia involvement (CSF with WBC greater than 5/mm\^3 and malignant cells on cytospin) * No consenting 5/6 or 6/6 HLA-matched related donor available * 3-6/6 HLA-matched unrelated umbilical cord blood donor available PATIENT CHARACTERISTICS: Age: * See Disease Characteristics * 18 and under Performance status: * Karnofsky 70-100%, if age 16 to 18 * Lansky 50-100%, if under age 16 Life expectancy: * Not specified Hematopoietic: * See Disease Characteristics Hepatic: * Bilirubin less than 2.5 mg/dL * SGOT less than 5 times upper limit of normal Renal: * Creatinine normal for age OR * Creatinine clearance or glomerular filtration rate greater than 50% lower limit of normal for age Cardiovascular: * If symptomatic: * LVEF greater than 40% (or shortening fraction greater than 26%) and improves with exercise OR * Shortening fraction greater than 26% Pulmonary: * If symptomatic: * DLCO, FEV\_1, and FEC greater than 45% predicted OR * Oxygen saturation greater than 85% on room air Other: * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * HIV negative * No uncontrolled viral, bacterial, or fungal infection PRIOR CONCURRENT THERAPY: Biologic therapy: * See Disease Characteristics * At least 1 year since prior allogeneic stem cell transplantation (SCT) with cytoreductive preparative therapy * At least 6 months since prior autologous SCT * No concurrent thrombopoietic growth factors Chemotherapy: * See Disease Characteristics * See Biologic therapy Endocrine therapy: * Not specified Radiotherapy: * Not specified Surgery: * Not specified