RATIONALE: Giving chemotherapy, such as busulfan, fludarabine, and melphalan, before a donor umbilical cord blood stem cell transplant helps stop the growth of abnormal or cancer cells and prepares the patient's bone marrow for the stem cells. When the healthy stem cells from a donor are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells. Giving cyclosporine and mycophenolate mofetil may stop this from happening.
PURPOSE: This phase II trial is studying how well combination chemotherapy followed by a donor umbilical cord blood transplant works in treating infants with high-risk acute leukemia or myelodysplastic syndromes.