**Core Concept:** Vasculitis, glomerulonephritis, and peripheral neuropathy are clinical syndromes that can occur due to various underlying causes. These manifestations are indicative of an immune-mediated systemic disorder.

**Why the Correct Answer is Right:** In this scenario, the correct answer is **C. Blood and urine cultures**, as these investigations are essential for identifying specific organisms causing these complications in cases of infectious causes. Blood cultures are important to isolate the causative organism for sepsis or endocarditis. Urine cultures are crucial for diagnosing urinary tract infections or pyelonephritis, which can lead to glomerulonephritis.

**Why Each Wrong Option is Incorrect:**

A. **Neutrophil elastase:** This enzyme is not relevant to diagnose the specific cause of vasculitis, glomerulonephritis, or peripheral neuropathy.

B. **Histopathology:** Although histopathology is essential for confirming the diagnosis in many cases, in this scenario, it is less specific for identifying the underlying cause of these clinical syndromes as a result of infections.

D. **Blood and urine cultures:** Though blood and urine cultures are important steps in the diagnostic process, the correct answer (option C) is more specific and comprehensive in identifying the causative organism responsible for these clinical syndromes.

**Clinical Pearl:** A thorough history, physical examination, and relevant investigations are crucial in determining the underlying cause of these clinical syndromes. Infections are a common cause, and performing blood and urine cultures is essential for identifying the causative organism. A well-rounded approach to diagnosis involves considering other potential causes, such as autoimmune diseases, drug reactions, or malignancies, but in this case, the correct answer focuses on identifying the infection.

**Correct Answer:** C. Blood and urine cultures