Step 1: The oestrogen in combined pills increases clotting factors, so the strongest reason to forbid them is an active or built-in clotting risk.
Step 2: Deep vein thrombosis directly demonstrates that the patient forms venous clots; adding a pro-coagulant pill could trigger pulmonary embolism, making DVT an absolute bar to use.
Step 3: The standard absolute-contraindication list also covers cardiovascular disease, inherited thrombophilia, heavy smokers above $40$ years, liver tumours or severe cirrhosis, and breast cancer.
Step 4: Renal disease and uncomplicated diabetes are weighed individually rather than being absolute bars, and amenorrhoea is not a contraindication. Hence DVT is the correct choice.
\[\boxed{\text{DVT}}\]