Busulfan, Antithymocyte Globulin, and Fludarabine Followed By a Donor Stem Cell Transplant in Treating Young Patients With Blood Disorders, Bone Marrow Disorders, Chronic Myelogenous Leukemia in First Chronic Phase, or Acute Myeloid Leukemia in First Remission

DISEASE CHARACTERISTICS: * Diagnosis of one of the following hematopoietic disorders: * Severe aplastic anemia with marrow aplasia (i.e., absolute neutrophil count \< 500/mm\^3, platelet and/or red blood cell transfusion dependent), meeting 1 of the following criteria: * Closely matched related donor * Unresponsive to immunosuppressive therapy within 3 months after follow-up AND alternative matched unrelated donor available * Congenital marrow failure syndrome, including any of the following: * Primary red blood cell aplasia (Diamond-Blackfan syndrome) * Congenital neutropenia (Kostmann's syndrome) * Amegakaryocytic thrombocytopenia * Hemoglobinopathy including any of the following: * β-thalassemia major * Sickle cell anemia * Severe immunodeficiency disease including any of the following: * Chediak-Higashi disease * Wiskott-Aldrich syndrome * Combined immunodeficiency disease (Nezelof's) * Hyperimmunoglobulin M syndrome * Bare lymphocyte syndrome * Other stem cell defects (e.g., osteopetrosis) * Chronic myelogenous leukemia in first chronic phase * Not eligible for other ongoing phase II/III studies * Acute myeloid leukemia in first remission * Not eligible for other ongoing phase II/III studies * Inborn errors of metabolism * No severe combined immunodeficiency disorder * Available donor, meeting 1 of the following criteria: * Related donor matched by high resolution DNA typing at both HLA Dr…