**Core Concept**
The question is testing the association between neurological symptoms and premature graying of hair, which is linked to a specific condition that affects the body's ability to regulate certain bodily functions.

**Why the Correct Answer is Right**
The condition associated with neurological symptoms and premature graying of hair is **Addison's disease**. This is due to the deficiency of cortisol and aldosterone hormones, which are produced by the adrenal glands. The adrenal glands are responsible for regulating various bodily functions, including the response to stress, metabolism, and electrolyte balance. In Addison's disease, the adrenal glands do not produce enough cortisol and aldosterone, leading to a range of symptoms, including neurological symptoms such as fatigue, weakness, and changes in mood, as well as premature graying of hair.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is not relevant to the association between neurological symptoms and premature graying of hair.
* **Option B:** This option is incorrect because it is not directly related to the symptoms described in the question.
* **Option D:** This option is incorrect because it is not the primary condition associated with neurological symptoms and premature graying of hair.

**Clinical Pearl / High-Yield Fact**
Addison's disease is often referred to as a "crisis of the adrenal glands" due to the dramatic and potentially life-threatening consequences of adrenal insufficiency.

**Correct Answer: C. Addison's disease**