Trane AC review: Paid for extended parts warranty, but they can't get the part and won't give any time estimate

I bought Trane's top end AC/Heat, which uses a computerized controller instead of a generic thermostat. The controller is no longer working correctly. The dealer is only being told it is on back order, with no estimate for arrival, and Trane's customer service won't give an answer and only says talk to the dealer. My extended parts warranty is with Trane and is not a third party warranty. Trane even pulled up my registered warranty. Seems like Trane should be willing to help their customer instead of passing the buck.