A 28-year-old woman with newly diagnosed type 1 diabetes mellitus is admitted with diabetic ketoacidosis (DKA). Her arterial blood gas shows pH 7.18, HCO₃⁻ 12 mEq/L, and blood glucose 520 mg/dL. Serum insulin is <2 mIU/mL (normal fasting: 5–15 mIU/mL) and glucagon is 850 pg/mL (normal fasting: 50–100 pg/mL). Which of the following best explains the profound hyperglycemia and ketosis despite the elevated glucagon level?