(e) Obturator hernia: This is the most likely diagnosis because obturator hernias are more common in elderly females and can cause small bowel obstruction without any previous surgery or external hernia. They are often difficult to diagnose and can be missed, leading to significant morbidity and mortality.

(b) Volvulus: Volvulus is a possible cause of small bowel obstruction in the elderly, especially if there is a history of chronic constipation or other factors that could lead to twisting of the bowel.
(c) Gallstone ileus: Gallstone ileus is another possible cause, where a gallstone passes through a fistula into the small intestine and obstructs it. This condition is more common in elderly females.
(a) Small bowel neoplasm: Although less common, small bowel neoplasms can cause obstruction, especially in the elderly population.

Abdominal abscess: Although listed as an option (d), an abdominal abscess is less likely to cause a mechanical small bowel obstruction directly but can lead to obstruction through adhesions or mass effect. It's crucial not to miss this diagnosis due to its potential for severe consequences if not treated promptly.
Intussusception: Not listed among the options but is a condition where a part of the intestine telescopes into another part, which can cause obstruction. It's more common in children but can occur in adults, often associated with a lead point such as a tumor.

Inflammatory bowel disease: Conditions like Crohn's disease can cause small bowel obstruction, but they are less common in the elderly without a previous diagnosis.
Internal hernias: These are rare and can cause small bowel obstruction but are less likely without any previous surgery.
Adhesions from previous intra-abdominal infections: Although the question specifies no previous surgery, adhesions from previous infections could potentially cause obstruction, but this would be less common and not as directly related to the question's criteria.