RATIONALE: Giving chemotherapy before a donor umbilical cord blood transplant (UCBT) helps stop the growth of cancer and abnormal cells and helps stop the patient's immune system from rejecting the donor's stem cells. When the stem cells from an unrelated donor, that do not exactly match the patient's blood, 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 antithymocyte globulin before transplant and cyclosporine and mycophenolate mofetil after transplant may stop this from happening.