Is this a frost-free faucet? If so, it could be leaking inside the house when you turn it on. The anti-siphon function would not prevent it from flowing water in most cases. Maybe one of the add-on ones could. If it is an add-on one, it's probably easier to just remove it and replace. A faucet with it built-in generally leaks when that fails, not block the flow. If there is a washer, it could be stuck, blocking the water.