**Core Concept**
The patient's presentation suggests a systemic vasculitis, characterized by inflammation of blood vessels, leading to organ damage and various clinical manifestations. The presence of palpable purpuric rash, hematuria, and arthralgia indicates a vasculitic process affecting multiple systems.

**Why the Correct Answer is Right**
The patient's symptoms are consistent with Henoch-Schönlein purpura (HSP), a form of vasculitis that primarily affects small vessels. HSP is characterized by the deposition of IgA immune complexes in the vessel walls, leading to inflammation and damage. The presence of normal coagulation tests rules out a coagulopathy as the cause of the purpuric rash. The combination of abdominal pain, hematuria, arthralgia, and palpable purpuric rash is classic for HSP.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option might be thinking of Systemic Lupus Erythematosus (SLE), which can also present with vasculitis, but SLE typically involves multiple organ systems and has a more complex serological profile.
* **Option B:** This option might be thinking of Thrombotic Thrombocytopenic Purpura (TTP), which is characterized by microangiopathic hemolytic anemia, thrombocytopenia, and renal failure, but TTP typically has abnormal coagulation tests and does not typically present with a palpable purpuric rash.
* **Option C:** This option might be thinking of Polyarteritis Nodosa (PAN), which is a form of vasculitis that primarily affects medium-sized vessels, but PAN typically presents with more severe hypertension and organ damage, and does not typically have a palpable purpuric rash.
* **Option D:** This option might be thinking of Kawasaki disease, which is a form of vasculitis that primarily affects children, but Kawasaki disease typically presents with fever, conjunctivitis, and cervical lymphadenopathy, and does not typically have a palpable purpuric rash.

**Clinical Pearl / High-Yield Fact**
Henoch-Schönlein purpura (HSP) is often associated with a preceding upper respiratory infection, and the deposition of IgA immune complexes in the vessel walls is a key pathophysiological mechanism.

**Correct Answer:** C.