OUTLINE: Patients receive a combination of 3 antiretroviral agents beginning at least 3 weeks prior to the initiation of the myeloablative conditioning regimen. The antiretroviral agents are discontinued on days -5 to -1 prior to transplant. Beginning on day 0 the antiretroviral agents are restarted and continue indefinitely. Patients who are given umbilical cord blood (UCB) transplants undergo collection of autologous peripheral blood stem cells (PBSC) prior to the myeloablative conditioning regimen in case there is UCB graft failure. Prior to PBSC or UCB transplantation on day 0, all patients receive a myeloablative conditioning regimen. The conditioning regimen consists of total body irradiation twice a day on days -9 to -5 and melphalan IV over 60 minutes on days -4 to -2. Patients receiving UCB transplant also receive anti-thymocyte globulin over 6 hours on days -3 to -1. Patients are followed every 3 months for 3 years, then annually for the next 3 years.