When I pull Tilt Chain, why don't my vertical blinds tilt?

There is a rotating element (usually a splined tube) that runs down the middle of the track, through each carrier. The tilt chain is attached to the end of the splined-tube rotating element and when the tilt chain is pulled, the rotating element turns (longitudinally/axially) and turns a ring gear within each carrier. The ring gear in the carrier mates with a pinion gear that the stem attaches to, causing the stem to rotate when the chain is pulled (i.e. causes the vanes to tilt).

Because it is very unlikely that every single ring & pinion carrier gearset is damaged, it is highly likely that the tilt chain mechanism is broken where it attaches to and rotates the splined-tube rotating element.