**Core Concept**
The patient is presenting with signs and symptoms suggestive of a liver disease, specifically a conjugated hyperbilirubinemia, which is often associated with obstructive jaundice. The presence of deep jaundice, hepatomegaly, and elevated conjugated bilirubin levels point towards an obstruction in the biliary system.

**Why the Correct Answer is Right**
The correct diagnosis in this case is likely a case of Biliary Atresia, a congenital anomaly of the biliary system where there is an obstruction of the bile ducts. The elevated conjugated bilirubin levels and the presence of bile pigments in the urine are indicative of a biliary obstruction. The liver function tests, including the elevated serum creatinine and low hemoglobin, suggest a severe liver dysfunction.

**Why Each Wrong Option is Incorrect**
* **Option A:** Serum Alkaline Phosphatase (ALP) is an important test in diagnosing biliary obstruction and is often elevated in cases of Biliary Atresia. It is not of least importance.
* **Option B:** Liver Function Tests (LFTs) are crucial in assessing the liver function and are often used to monitor the progression of liver disease. They are not of least importance in this case.
* **Option C:** Serum Bilirubin levels are a critical parameter in diagnosing jaundice and are often used to monitor the effectiveness of treatment. They are not of least importance.
* **Option D:** White Blood Cell Count (WBC) is not a specific test for diagnosing liver disease or biliary obstruction. It is often used to assess the presence of infection or inflammation, which is not the primary concern in this case.

**Clinical Pearl / High-Yield Fact**
In cases of biliary obstruction, the liver function tests can be used to monitor the progression of the disease and the effectiveness of treatment. It's essential to note that the liver function tests can be abnormal even in the absence of jaundice, and a high index of suspicion is required to diagnose biliary obstruction.

**Correct Answer: D. White Blood Cell Count (WBC) is of least importance to diagnose this case.**