Something's gotta be pretty resilient if the dead are still walking around!
What if it's closer to the Vashta Nerada idea? A bacteria that infests every cell and forces the movement? But you'd still have the problem of feeding the bacteria...if there's no fresh food and it can't eat itself (or the dead), why doesn't the bacteria die? Maybe the sitting zombie was dormant (that is, the bacteria inside the zombie was dormant making the zombie dormant), but then wouldn't more of the zombies be dormant by now?