Combination Chemotherapy and Total-Body Irradiation Before Donor Umbilical Cord Blood Transplant in Treating Patients With Advanced Hematologic Cancer, Metastatic Breast Cancer, or Kidney Cancer

DISEASE CHARACTERISTICS: * Diagnosis of 1 of the following: * Acute myeloid leukemia (AML), meeting 1 of the following criteria: * In first complete remission (CR1) by morphology AND at high risk, as evidenced by 1 of the following: * AML secondary to myelodysplastic syndromes (MDS) * High-risk cytogenetics, such as those associated with MDS or complex karyotype * More than 2 courses of therap were required to obtain a CR * In second or greater CR by morphology * In morphologic relapse or persistent disease, defined as \> 5% blasts in normocellular bone marrow OR any percentage of blasts if blasts have unique morphologic markers (e.g., auer rods) * In cytogenetic relapse (without morphologic relapse) * Acute lymphoblastic leukemia (ALL), meeting 1 of the following criteria: * In CR1 by morphology AND at high risk, as evidenced by 1 of the following: * High-risk cytogenetics, such as t(9;22), t(1;19), t(4;11), or other MLL rearrangements * More than 1 course of therapy was required to obtain a CR * In second or greater CR by morphology * In morphologic relapse or persistent disease as defined for AML * In cytogenetic relapse (without morphologic relapse) * Chronic myelogenous leukemia * All types allowed except refractory blast crisis * Non-Hodgkin's lymphoma (NHL) * No intermediate- or high-grade NHL or mantle cell NHL that is progressive on salvage therapy * Stable disease allowed provi…