Immunoablative Mini Transplant (Hematopoietic Peripheral Blood Stem Cell Transplant [HPBSC])

Inclusion Criteria: * Patients with recurrent solid tumors * Patients with malignant melanoma * Patients with hematological malignancies. * Chronic myelogenous leukemia in chronic or accelerated phase, to include chronic myelomonocytic leukemia (juvenile chronic myelogenous leukemia (JCML) or CMML). * Acute lymphoblastic leukemia (ALL) * First remission high-risk ALL (Ph+ with initial high white blood cell (WBC)t (4-11) in infants less than 1 year and CALLA negative) * Second or subsequent remission ALL or isolated extramedullary disease on or off therapy. * Acute non-lymphocytic leukemia (ANLL) * Patients with ANLL in first remission who have a matched sibling donor. * ANLL in second remission, or patients who only achieve an initial partial remission \< 15% blasts, or early relapse. * Myelodysplastic syndromes (MDS): refractory anemia (RA), refractory anemia with excess blasts (RAEB), refractory anemia with excess blasts in transformation (RAEB-T) and CMML/JCML. * Selected immunodeficiencies: * Wiskott-Aldrich syndrome. * Severe combined immunodeficiency variants that require ablation. * Hyper-Immunoglobulin M (IgM) syndrome. * Other immune deficiencies after approval from the medical director. * Bone marrow failure syndromes (single or multiple hematopoietic lines) * Venous access: A double lumen central vascular access device or its equivalent will be required for all patients entered on the protocol. * Informed consent: The donor and the patient and/or the patient's legally authorized guardian must acknowledge in writing that consent to become a study subject has been obtained in accordance with the institutional policy approved by the United States (U.S.) Department of Health and Human Services. * Patient organ function requirements: * Adequate renal function: serum creatinine \< 2 x normal, or creatinine clearance calculated by Schwartz formula, of glomerular filtration rate (GFR) \> 40 ml/min/1.73m2, or an equivalent GFR as determined by the institutional normal range. * Adequate liver function: total bilirubin \</= 2 x normal; and Aspartate aminotransferase (AST) or Alanine aminotransferase (ALT) \</= 4 x normal. * Adequate cardiac function: shortening fraction of \> 24% by echocardiogram, or ejection fraction of \> 30% by radionuclide angiogram. * Adequate pulmonary function: Diffusion Lung Capacity Carbon Monoxide (DLCO), Forced Expiratory Volume in 1 second (FEV1) / Forced Vital Capacity (FVC) \> 30% by pulmonary function test. For children who are uncooperative for pulmonary function tests and have no evidence of dyspnea at rest or exercise intolerance, pulse oximetry \> 94% on room air is considered acceptable. * Performance status: Lansky Score \>/= 60% for children \</= 16 years of age; or Karnofsky \> 60% status for those \> 16 years of age. Exclusion Criteria: * Patients who are pregnant * Inability to find a suitable donor for the patient * Patient is HIV-positive * Patient has active Hepatitis B * Disease progression or relapse prior to HPC infusion