RATIONALE: Antiviral agents are drugs that act against viruses and may be an effective treatment for HIV. Peripheral stem cell transplantation or umbilical cord blood transplantation may be able to replace immune cells that were destroyed by chemotherapy and radiation therapy used to kill tumor cells. Combining either umbilical cord blood transplantation or peripheral stem cell transplantation with antiviral therapy may be an effective treatment for HIV-positive patients who have hematologic cancer.