Donor Umbilical Cord Blood Transplantation in Treating Patients With Leukemia, Lymphoma, or Nonmalignant Hematologic Disorders

DISEASE CHARACTERISTICS: Diagnosis of 1 of the following hematologic malignancies: Acute myeloid leukemia (AML)* With or without history of myelodysplastic syndromes (MDS) Patients in first complete remission (CR) (no greater than 5% blasts in marrow) with translocations t(8;21) and inv(16) are allowed provided they failed first-line induction therapy Patients in first CR (no greater than 5% blasts in marrow) with translocations t(15;17) are allowed provided at least 1 of the following is true: Failed first-line induction therapy Molecular evidence of persistent disease No patients in first CR and with Down syndrome Acute lymphoblastic leukemia (ALL)*, meeting 1 of the following criteria: Not in first CR (no greater than 5% blasts in marrow) In first CR and high risk as defined by 1 of the following: Hypoploidy (no more than 44 chromosomes) Pseudodiploidy with translocations or molecular evidence of t(9;22), 11q23, or t(8;14) (excluding B-ALL) or +MLL gene rearrangement One of the following elevated WBC levels: WBC greater than 100,000/mm^3 if 6 to 12 months of age WBC greater than 200,000/mm^3 if between 10 and 17 years of age WBC greater than 20,000/mm^3 if 18 years of age and over (adult [over 18 years of age] patient stratum closed to accrual) Failed to achieve CR after 4 weeks of induction therapy B-ALL that is not in first CR or that meets at least 1 of the high-risk criteria specified above No translocation t(8;14) No blasts with surface immunoglobulins CD10 negative Undifferentiated leukemia* Infant leukemia* Biphenotypic leukemia* Chronic myelogenous leukemia, meeting 1 of the following criteria: Accelerated phase Chronic phase At least 1 year from diagnosis without an identified matched unrelated bone marrow donor AND unresponsive to or unable to tolerate interferon Blast crisis* (greater than 30% promyelocytes plus blasts in the marrow) One of the following MDS: Refractory anemia Refractory anemia with ringed sideroblasts Refractory anemia with excess blasts (RAEB) RAEB in transformation Chronic myelomonocytic leukemia Paroxysmal nocturnal hemoglobinuria Hodgkin's or non-Hodgkin's lymphoma beyond first CR or failed primary induction therapy Tumor displays chemosensitivity (greater than 50% reduction in mass size after the most recent therapy) NOTE: *Patients in third or greater medullary relapse or refractory disease (other than primary induction failures) or blast crisis receive the study busulfan/melphalan conditioning regimen) OR Diagnosis of one of the following nonmalignant diseases : Acquired severe aplastic anemia (stratum closed to accrual) Unresponsive to medical therapy with anti-thymocyte globulin and/or cyclosporine Inborn errors of metabolism, including, but not limited to the following: Hurler's syndrome Adrenoleukodystrophy Maroteaux-Lamy syndrome Globoid cell leukodystrophy Metachromatic leukodystrophy Fucosidosis Mannosidosis Fanconi anemia documented by increased chromosomal fragility assays and meeting 1 of the following criteria (stratum closed to accrual): Severe pancytopenia Absolute neutrophil count less than 500/mm^3 Platelet count less than 20,000/mm^3 Hemoglobin less than 8 g/dL Morphologic evidence of MDS with clonal chromosomal abnormalities Leukemia transformation Other marrow failure syndromes, including any of the following (stratum closed to accrual): Blackfan-Diamond syndrome that is unresponsive to medical therapy Kostmann's congenital agranulocytosis unresponsive to medical therapy Congenital amegakaryocytic thrombocytopenia Thrombocytopenia absent radius Combined immune deficiencies including, but not limited to the following: Severe combined immunodeficiency (SCID) 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 Nezeloff's syndrome Cartilage hair hypoplasia Reticular dysgenesis No active CNS leukemia (cerebrospinal fluid with WBC greater than 5/mm^3 and malignant cells on cytospin) No SCID patients who do not require cytoreduction No dyskeratosis congenita No primary myelofibrosis No grade 3 or greater myelofibrosis Familial erythrophagocytic lymphohistiocytosis patients must not have any of the following: Abnormal brain MRI Neurologic symptoms Lymphocytes and monocytes greater than 7/mm^3 in the cerebrospinal fluid No available 5/6 or 6/6 HLA-matched related donor PATIENT CHARACTERISTICS: Age 55 and under (over 18 closed to accrual) Performance status Karnofsky 70-100% OR Lansky 50-100% (patients under 16 years old) Life expectancy Not specified Hematopoietic See Disease Characteristics Hepatic SGOT less than 5 times upper limit of normal Bilirubin less than 2.5 mg/dL Renal Creatinine normal for age OR Creatinine clearance or glomerular filtration rate greater than 50% of lower limit of normal Cardiovascular LVEF greater than 40% at rest and must improve with exercise* OR Shortening fraction greater than 26%* NOTE: *If symptomatic Pulmonary DLCO greater than 45% of predicted* (corrected for hemoglobin) FEV_1 and FEC greater than 45% of predicted (corrected for hemoglobin) OR Room air oxygen saturation greater than 85%* NOTE: *If symptomatic Other Not pregnant or nursing Negative pregnancy test Fertile patients must use effective contraception No uncontrolled viral, bacterial, or fungal infection HIV negative PRIOR CONCURRENT THERAPY: Biologic therapy See Disease Characteristics More than 12 months since prior allogeneic stem cell transplantation with cytoreductive preparative therapy More than 6 months since prior autologous stem cell transplantation Chemotherapy See Biologic therapy Endocrine therapy Not specified Radiotherapy Not specified Surgery Not specified Other No prior enrollment on this study No continuous life support (e.g., mechanical ventilation) within 1 year after study transplantation (for patients with inborn errors of metabolism)