Cisplatin or Carboplatin and Sorafenib in Treating Patients With Liver Cancer That Cannot Be Removed By Surgery

DISEASE CHARACTERISTICS: * Histologically confirmed hepatocellular carcinoma (HCC) OR serum alpha fetoprotein ≥ 400 ng/mL with radiological evidence suggestive of HCC * Unresectable disease * Child-Pugh class A or selected Child-Pugh class B disease (Child-Pugh score ≤ 7 points) * No Child-Pugh class C disease * No disease outside the liver or macroscopic invasion of the major vessels such as the portal vein * No known brain metastasis * Patients with neurological symptoms must undergo CT scan or MRI of the brain PATIENT CHARACTERISTICS: * ECOG performance status 0-1 * WBC ≥ 3,000/mm³ (for patients scheduled to receive carboplatin) or ≥ 2,000/mm³ (for patients scheduled to receive cisplatin) * Platelet count ≥ 100,000/mm³ (for patients scheduled to receive carboplatin) or ≥ 60,000/mm³ (for patients scheduled to receive cisplatin) * Serum creatinine ≤ 1.9 mg/dL (for patients scheduled to receive carboplatin) or ≤ 1.5 mg/dL (for patients scheduled to receive cisplatin) * Serum total bilirubin ≤ 3 mg/dL * AST and ALT \< 5 times upper limit of normal * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for ≥ 3 months after completion of study treatment * No cardiac disease, including any of the following: * NYHA class III-IV congestive heart failure * Unstable angina (anginal symptoms at rest) * New onset of angina within the past 3 months * Myocardial infarction within the past 6 months * Cardiac ventricular arrhythmias requiring anti-arrhythmic therapy * No uncontrolled hypertension, defined as systolic BP \> 150 mm Hg or diastolic BP \> 90 mm Hg, despite optimal medical management * No thrombolic or embolic events (e.g., cerebrovascular accident, including transient ischemic attacks) within the past 6 months * No pulmonary hemorrhage/bleeding event ≥ CTCAE grade 2 within the past 4 weeks * No other hemorrhage/bleeding event ≥ CTCAE grade 3 within the past 4 weeks * No evidence or history of bleeding diathesis or coagulopathy * No evidence of encephalopathy * No condition that would impair the ability to swallow whole pills * No history of malabsorption problems * No significant traumatic injury within the past 4 weeks * No serious non-healing wound, ulcer, or bone fracture * No active clinically serious infection * No known HIV infection * No known or suspected allergy to sorafenib tosylate or any other study agent PRIOR CONCURRENT THERAPY: * No prior cisplatin, carboplatin, or sorafenib tosylate * No prior systemic chemotherapy for HCC * No other prior systemic or locoregional therapy * More than 4 weeks since prior major surgery or open biopsy * No concurrent St. John's wort or rifampin