Donor Umbilical Cord Blood Transplant in Treating Patients With Advanced Hematological Cancer or Other Disease

DISEASE CHARACTERISTICS: * Diagnosis of advanced hematologic malignancy or other disease not curable by conventional chemotherapy, including any of the following: * Acute myeloid leukemia in complete remission (CR)\* (as defined by hematologic recovery, \< 5% blasts in the bone marrow by morphology, and a cellularity of \> 15%), meeting one of the following criteria: * In first complete remission (CR1) AND has high-risk disease as evidenced by any of the following: * Preceding myelodysplastic syndromes (MDS) * High-risk cytogenetics (e.g., monosomy 5 or 7, or as defined by referring institution treatment protocol) * Required \> 2 courses of therapy to obtain CR * Erythroblastic or megakaryocytic leukemia * In second CR (CR2) or beyond * Acute lymphoblastic leukemia in CR\* (as defined by hematologic recovery, \< 5% blasts in the bone marrow by morphology, and a cellularity of \> 15%), meeting one of the following criteria: * In CR1 AND has high-risk disease as evidenced by any of the following: * t(9;22), t(1;19), t(4;11), or other MLL rearrangements * Hyplodiploid * Required \> 1 course of therapy to obtain CR * Beyond CR2 * Chronic myelogenous leukemia (CML) * All types are allowed (except refractory blast crisis CML) * Patients in chronic phase CML must have failed or been intolerant to prior imatinib mesylate (Gleevec) or other tyrosine kinase inhibitors * MDS * Any subtype allowed (incl…