RATIONALE: Giving chemotherapy before a donor umbilical cord blood stem cell transplant helps stop the growth of tumor cells. It also helps stop the patient's immune system from rejecting the donor's stem cells when they do not exactly match the patient's blood. The donated stem cells may replace the patient's immune cells and help destroy any remaining tumor cells (graft-versus-tumor effect). Sometimes the transplanted cells from a donor can also make an immune response against the body's normal cells. Giving cyclosporine and methylprednisolone after the transplant may stop this from happening.