SCID Bu/Flu/ATG Study With T Cell Depletion

This is a pilot clinical trial of hematopoietic stem cell transplantation for patients with a diagnosis of Severe Combined Immune Deficiency (SCID) who do not have an HLA-matched sibling donor. The stem cells will be derived from a 1) matched unrelated donor (MUD), 2) unrelated cord blood donor, or 3) a haplo-identical (parental) donor (in descending order of preference).Patients will receive a novel conditioning regimen with Busulfan, Fludarabine and Anti-thymocyte globulin (ATG) followed by an unrelated donor hematopoietic stem cell transplant (HSCT) with T-cell depletion using the CliniMACS device.