**Core Concept**
The patient presents with a classic triad of symptoms: palpable purpuric skin lesions, joint pain, and hematuria (blood in the urine), which suggests a systemic vasculitis. The presence of IgA deposits in the walls of small blood vessels, as seen on skin biopsy, points towards a specific immune-mediated disease.

**Why the Correct Answer is Right**
The patient's symptoms are characteristic of IgA vasculitis (also known as Henoch-Schönlein purpura), a type of small vessel vasculitis that primarily affects children. The deposition of IgA immune complexes in the walls of small blood vessels leads to inflammation and damage, resulting in the observed symptoms. The presence of RBC casts in the urine and elevated serum creatinine levels indicates kidney involvement, which is a common complication of IgA vasculitis. The positive stool guaiac test suggests gastrointestinal involvement, which is also consistent with IgA vasculitis.

**Why Each Wrong Option is Incorrect**

**Option A:** While Henoch-Schönlein purpura is a type of systemic vasculitis, the presence of ANCA (anti-neutrophil cytoplasmic antibodies) is more commonly associated with other forms of vasculitis, such as granulomatosis with polyangiitis (GPA) or microscopic polyangiitis (MPA). ANCA-negative vasculitis is more typical of IgA vasculitis.

**Option B:** Systemic lupus erythematosus (SLE) is a systemic autoimmune disease that can present with a wide range of symptoms, including skin rashes, joint pain, and kidney involvement. However, the specific pattern of IgA deposits in the skin and the absence of other characteristic SLE features (such as anti-dsDNA antibodies or antinuclear antibodies) make this diagnosis less likely.

**Option C:** Kawasaki disease is an acute vasculitis that primarily affects children and presents with fever, rash, and lymphadenopathy. While it can involve the kidneys, the presence of IgA deposits in the skin and the specific pattern of symptoms (palpable purpura, joint pain, and hematuria) are more consistent with IgA vasculitis.

**Option D:** Polyarteritis nodosa (PAN) is a systemic vasculitis that primarily affects medium-sized arteries. While it can present with a wide range of symptoms, including skin rashes and kidney involvement, the presence of IgA deposits in the skin and the specific pattern of symptoms are more consistent with IgA vasculitis.

**Clinical Pearl / High-Yield Fact**
IgA vasculitis is a classic example of a small vessel vasculitis that primarily affects children and is characterized by the deposition of IgA immune complexes in the walls of small blood vessels. Remember the classic triad of symptoms: palpable purpura, joint pain, and hematuria.

**Correct Answer:** C. IgA vasculitis (Henoch-Schönlein purpura).