Medullary nephrocalcinosis: This condition is characterized by the deposition of calcium salts within the renal medulla, which can be visualized as hyperdense renal pyramids on CT scans. The patient's symptoms and imaging findings, particularly the hyperdense renal pyramids, make this a strong consideration.

Variant of normal renal anatomy or function: Some individuals may have naturally denser renal pyramids that could be mistaken for pathology. Ultrasound, being more sensitive, can help differentiate between normal variants and true pathology.
Obstruction of the colon: Given the obstipation (severe constipation) of the colon, there could be an underlying cause such as a mechanical obstruction that needs to be evaluated further.

Uric acid nephropathy: Although less common, this condition can cause renal colic and could be associated with hyperdense renal pyramids if there are uric acid stones. Missing this diagnosis could lead to inappropriate management and worsening renal function.
Sarcoidosis: This systemic disease can cause nephrocalcinosis among other manifestations. While less likely, it's a diagnosis that could have significant implications if missed, given its systemic nature and potential for serious complications.

Primary hyperoxaluria: A rare genetic disorder leading to excessive oxalate production, which can cause nephrocalcinosis. This condition is rare but would be critical to identify due to its potential for severe renal damage and the availability of specific treatments.
Alport syndrome with nephrocalcinosis: A genetic disorder affecting the type IV collagen in the kidneys, which can lead to nephrocalcinosis among other renal manifestations. While rare, identifying this condition is crucial for managing renal disease progression and considering family screening.