Hepatic Encephalopathy with Coagulopathy: This condition is a likely cause given the patient's liver failure. Hepatic encephalopathy can lead to unresponsiveness, and coagulopathy associated with liver disease can cause severe subconjunctival hemorrhages without exterior trauma.

Uremic Encephalopathy: Kidney failure can lead to uremic encephalopathy, causing unresponsiveness. Although less directly linked to subconjunctival hemorrhages, the overall clinical picture of multi-organ failure makes this a plausible consideration.
Disseminated Intravascular Coagulation (DIC): Given the liver and kidney failure, DIC is a possible complication. It can cause both coagulopathy leading to subconjunctival hemorrhages and contribute to organ dysfunction, including the brain, leading to unresponsiveness.
Sepsis: Sepsis can cause multi-organ failure, including liver and kidney dysfunction, and can lead to coagulopathy and encephalopathy, explaining the patient's symptoms.

Cerebral Hemorrhage: Although the question specifies no signs of exterior trauma, a cerebral hemorrhage could cause unresponsiveness and, through increased intrathoracic pressure, lead to subconjunctival hemorrhages. This diagnosis is critical to rule out due to its high morbidity and mortality.
Meningitis or Encephalitis: Infections of the central nervous system can cause unresponsiveness and, in rare cases, could be associated with subconjunctival hemorrhages, especially if there's a coagulopathy component.
Thrombotic Thrombocytopenic Purpura (TTP): TTP can cause multi-organ failure, including neurological symptoms and coagulopathy, which might fit the patient's presentation.

Vitamin K Deficiency: Although less common, a severe vitamin K deficiency could lead to coagulopathy, causing subconjunctival hemorrhages. However, it would be unusual for this to be the primary cause of unresponsiveness in the context of liver and kidney failure.
Amyloidosis: Systemic amyloidosis can involve multiple organs, including the liver and kidneys, and can cause coagulopathy. However, it's a rare condition and would be an unusual cause of the acute presentation described.
Purpura Fulminans: This is a rare, life-threatening condition characterized by extensive thrombosis and hemorrhagic necrosis of the skin, which could potentially cause subconjunctival hemorrhages. It's often associated with severe infections or genetic predispositions.