The purpose of this study is to evaluate the likely safety and effectiveness of danaparoid sodium versus argatroban for patients suffering from heparin-induced thrombocytopenia (HIT). Patients with HIT will have low blood platelet counts due to being given the medication heparin. Adult and pediatric participants who are determined to be eligible to participate will be assigned by chance to treatment with danaparoid sodium or argatroban. The study drugs are administered through intravenous therapy (IV). Study and safety assessments, including blood draws and compression ultrasounds, will be completed at study visits. Participants will be in this study for at least 45 days, but could receive treatment longer depending on HIT severity. You will be hospitalized while you are receiving study drug treatment for a minimum fo 14 days. You will have 4 study follow-up visits after they have been discharged from the hospital.