Intussusception: This condition is a common cause of intestinal obstruction in children, especially in the 6-36 month age range. The presence of a hard, immobile lump (possibly representing the intussusceptum), abdominal pain, and the absence of bowel movements for the last 2 days are highly suggestive of intussusception. The lack of immunization increases the risk due to the potential for viral infections that can lead to intussusception.

Constipation with fecal impaction: Although the child has been having daily bowel movements until the last 2 days, constipation can sometimes present with a palpable abdominal mass. The pain and absence of recent bowel movements could support this diagnosis, but the description of the lump as hard and immobile is less typical.
Wilms Tumor: This is a type of kidney cancer that can present as an abdominal mass in children. It's more common in slightly older children but should be considered, especially given the description of the mass as hard and immobile.
Neuroblastoma: Another type of cancer that can present with an abdominal mass, neuroblastoma is a consideration, especially in young children. The mass can be hard and fixed, and abdominal pain is a common symptom.

Appendicitis: Although less common in children under 3, appendicitis can present with abdominal pain and potentially a palpable mass if the appendix is retrocecal or if there's significant inflammation. Missing this diagnosis could lead to perforation and severe consequences.
Volvolus or midgut volvulus: These conditions involve twisting of the intestine and can present with severe abdominal pain, vomiting, and sometimes a palpable mass. They are surgical emergencies.
Incarcerated or strangulated hernia: If the child has an inguinal hernia that becomes incarcerated or strangulated, it could present with severe pain and a hard, immobile lump. This is a surgical emergency.

Rhabdomyosarcoma: A soft tissue cancer that can present as an abdominal mass, though it's much less common than other diagnoses listed here.
Lymphoma: Can present with an abdominal mass, but it's rare in this age group and would typically be associated with other systemic symptoms.
Teratoma or other germ cell tumors: These can present as abdominal masses but are less common and might have additional symptoms depending on their location and effect on surrounding structures.