In more than 120 instances, General Motors was forced under state lemon laws to buy back faulty Cobalts, pay settlements to owners or let them trade in the cars, an analysis by The New York Times of state databases and court records shows. The buybacks came as dozens of claims were filed separately at G.M. from 2005 to 2009 that fit a specific pattern — moving cars, sometimes traveling at high speeds, would suddenly stop working.