Have you tried the input reset? It's mostly recommended for the dock, but may help in your case. Hold the volume '-' button and the "..." menu buttons for 5 seconds. After the beep, disconnect and reconnect all your devices.
They should not need to replace the entire engine, unless they are shop-level components. The airlines will have records for each part, and they should be able to narrow down what engines received specific parts from that manufacturer.
Have you tried the input reset? It's mostly recommended for the dock, but may help in your case. Hold the volume '-' button and the "..." menu buttons for 5 seconds. After the beep, disconnect and reconnect all your devices.