Constipation: This is the most likely diagnosis given the symptoms of no bowel movement for 4 days, which can cause left lower quadrant pain due to the accumulation of feces in the sigmoid colon.

Diverticulitis: Inflammation of the diverticula in the sigmoid colon can cause left lower quadrant pain and changes in bowel habits, including constipation.
Irritable Bowel Syndrome (IBS): Although IBS can present with a variety of symptoms, constipation-predominant IBS could lead to left lower quadrant pain and decreased bowel movements.
Sigmoid Volvulus: A condition where the sigmoid colon twists on itself, which can cause severe abdominal pain, constipation, and obstruction.

Intestinal Obstruction: A mechanical blockage of the intestine that can cause severe abdominal pain, constipation, and vomiting. Early diagnosis is crucial to prevent complications.
Appendicitis (if pain has shifted): Although appendicitis typically presents with right lower quadrant pain, it can occasionally present atypically, especially if the appendix is retrocecal or if the pain has shifted.
Ectopic Pregnancy: In women of childbearing age, ectopic pregnancy can cause lower abdominal pain and changes in bowel habits due to the proximity of the fallopian tubes to the intestines.
Ovarian Torsion: A gynecological emergency that can cause severe lower abdominal pain and can be associated with changes in bowel habits due to the shared innervation of the ovaries and intestines.

Colonic Cancer: Although less common, colonic cancer can cause changes in bowel habits, including constipation, and abdominal pain, especially if the tumor is located in the sigmoid colon.
Inflammatory Bowel Disease (IBD): Conditions like Crohn's disease or ulcerative colitis can cause chronic abdominal pain, changes in bowel habits, and other systemic symptoms.
Ischemic Colitis: Reduced blood flow to the colon can cause abdominal pain, changes in bowel habits, and potentially life-threatening complications if not promptly addressed.