Viral Hepatitis: This condition can lead to both a low white blood count (leukopenia) due to the bone marrow's response to the virus and elevated bilirubin levels as a result of liver inflammation and dysfunction. The combination of these symptoms, especially in the context of other signs like jaundice and liver enzyme elevations, makes viral hepatitis a strong candidate.

Sepsis: Although sepsis can cause an elevated white blood cell count, in some cases, especially in the elderly or those with compromised immune systems, it can lead to leukopenia. Elevated bilirubin can occur due to liver dysfunction secondary to the septic process. The clinical context, including signs of infection and organ dysfunction, would support this diagnosis.
Hemolytic Anemia: Conditions that cause the destruction of red blood cells can lead to elevated bilirubin levels (due to the breakdown of hemoglobin) and potentially a low white blood count if the bone marrow is affected or if there's an associated infection or inflammation. Examples include autoimmune hemolytic anemia or drug-induced hemolysis.
Liver Cirrhosis: Advanced liver disease can cause a decrease in the production of white blood cells and an increase in bilirubin due to the liver's compromised ability to process and excrete bilirubin. Other signs of cirrhosis, such as ascites, varices, and hepatic encephalopathy, would support this diagnosis.

Malaria: Although less common in certain regions, malaria can cause both hemolysis (leading to elevated bilirubin) and bone marrow suppression (resulting in leukopenia). Given its potential severity and the importance of prompt treatment, it's crucial not to miss this diagnosis, especially in travelers to endemic areas.
Toxins or Medications: Certain drugs and toxins can cause bone marrow suppression and liver dysfunction, leading to the observed laboratory abnormalities. Identifying and removing the offending agent is critical for treatment.
Severe Bacterial Infections: Certain bacterial infections, such as typhoid fever or brucellosis, can affect the bone marrow and liver, leading to leukopenia and elevated bilirubin. These conditions require specific antibiotic treatments.

Lymphoma or Leukemia: Although more commonly associated with elevated white blood cell counts, certain types of lymphoma or leukemia can present with leukopenia and liver involvement, leading to elevated bilirubin.
Wilson's Disease: A genetic disorder that leads to copper accumulation in the liver and other organs, potentially causing liver dysfunction and hemolysis. It's rare but important to consider in young patients with unexplained liver disease and hemolytic anemia.
Paroxysmal Nocturnal Hemoglobinuria (PNH): A rare, acquired, life-threatening disease of the blood characterized by the destruction of red blood cells (hemolysis), bone marrow failure, and the potential for thrombotic events. It can present with elevated bilirubin due to hemolysis and leukopenia due to bone marrow failure.