**Core Concept**
The underlying condition is likely Hirschsprung's disease, a congenital disorder affecting the colon's ability to function due to the absence of ganglion cells in the distal colon and rectum. This leads to a functional obstruction, causing symptoms such as constipation and dilated proximal colon.

**Why the Correct Answer is Right**
In Hirschsprung's disease, the absence of ganglion cells in the rectosigmoid region results in a failure of the normal peristaltic movement of the colon. This leads to a functional obstruction, causing the proximal colon to dilate. The absence of stool in the rectal ampulla is a classic finding in this condition, as the affected segment of the colon is incapable of propelling stool into the rectum. The clinical presentation in a newborn with Down syndrome, who is at increased risk of Hirschsprung's disease, further supports this diagnosis.

**Why Each Wrong Option is Incorrect**
**Option A:** This option does not provide a plausible explanation for the patient's symptoms and findings. While it is a type of gastrointestinal obstruction, it is not directly related to the absence of ganglion cells in the colon.

**Option B:** This option refers to a different type of gastrointestinal obstruction caused by a mechanical blockage, such as intussusception or volvulus. However, the patient's symptoms and radiographic findings are more consistent with a functional obstruction, rather than a mechanical one.

**Option C:** This option is not directly related to the patient's symptoms and findings. While it is a type of gastrointestinal motility disorder, it is not typically associated with the absence of ganglion cells in the colon.

**Option D:** This option is not a valid diagnosis for the patient's symptoms and findings. While it is a type of gastrointestinal condition, it is not directly related to the absence of ganglion cells in the colon.

**Clinical Pearl / High-Yield Fact**
Hirschsprung's disease is a congenital condition that can be associated with Down syndrome, and it is essential to consider this diagnosis in newborns with constipation and dilated proximal colon on radiograph.

**Correct Answer:** C.