**Core Concept**
The question is testing the student's knowledge of the anatomy and innervation of the muscles responsible for flexion of the distal interphalangeal joints of the fingers. The correct answer requires an understanding of the muscles and their innervation that control finger movement.

**Why the Correct Answer is Right**
The distal interphalangeal joints of the fingers are primarily flexed by the flexor digitorum profundus muscle. This muscle is innervated by the ulnar nerve for the fourth and fifth digits. The patient's inability to flex these joints suggests damage to the ulnar nerve, which is responsible for innervating the flexor digitorum profundus muscle. The ulnar nerve runs through the cubital tunnel at the elbow and can be damaged in cases of trauma, such as the one described.

**Why Each Wrong Option is Incorrect**
* **Option A:** The flexor digitorum superficialis muscle is primarily responsible for flexion of the proximal interphalangeal joints, not the distal interphalangeal joints.
* **Option B:** The lumbricals muscles are involved in flexion and extension of the fingers, but they are not primarily responsible for flexion of the distal interphalangeal joints.
* **Option D:** The extensor digitorum muscle is responsible for extension of the fingers, not flexion.

**Clinical Pearl / High-Yield Fact**
The ulnar nerve is commonly damaged in cases of trauma to the elbow, such as cubital tunnel syndrome or a direct blow to the elbow. This can result in weakness or paralysis of the intrinsic muscles of the hand, including the flexor digitorum profundus muscle.

**Correct Answer:** C.