DISEASE CHARACTERISTICS: Histologically confirmed diagnosis of one of the following: - Severe aplastic anemia with bone marrow cellularity less than 20% and at least 2 of the following criteria: Granulocyte count less than 500/mm3 Platelet count less than 20,000/mm3 Reticulocyte count less than 50,000/mm3 Etiologies may be Fanconi's anemia, hypoplastic leukemia, monosomy 7, drug exposure (chloramphenicol, NSAIDS), viral exposure (EBV, hepatitis, parvovirus, HIV), nutritional deficiencies, thymoma, paroxysmal nocturnal hemoglobinuria, and amegakaryocytic thrombocytopenia - Myelodysplastic syndrome (MDS) that is refractory to medical management or with cytogenetic abnormalities predictive of transformation into acute leukemia, including 5q-, 7q-, monosomy 7, and trisomy 8 De novo primary or therapy-related secondary MDS Refractory anemia or refractory anemia with ringed sideroblasts only - Inherited hematopoietic disorders that are refractory to medical management Severe combined immunodeficiency Familial erythrophagocytic lymphohistiocytosis Wiskott-Aldrich syndrome Kostmann's syndrome (infantile agranulocytosis) Chronic granulomatous disease Leukocyte adhesion deficiency Chediak-Higashi syndrome Paroxysmal nocturnal hemoglobinuria Fanconi's anemia Dyskeratosis congenita Diamond-Blackfan anemia Amegakaryocytic thrombocytopenia Osteopetrosis Gaucher's disease Lesch-Nyhan syndrome Mucopolysaccharidoses Lipidoses Must also meet all the following conditions: No HLA-ABC/DR identical related bone marrow or UCB donor No 5/6 antigen matched related bone marrow or UCB donor Condition precludes waiting to search and find a donor in the National Marrow Donor Registry Must have backup autologous or haploidentical related marrow Must have available serologic match umbilical cord blood unit in the New York Blood Center's Placental Blood Project