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What actually happens with this transmission is a failure of the turbine speed sensor located on the electrics plate of the valve body. It causes this "limp" mode as a sort of self protection. It is a very common problem on the early suv models unfortunately. I would recommend getting the fault codes scanned of the transmission computer and if there is indeed a turbine speed sensor fault, the whole electrics plate will have to be ordered from a dealership and programmed. The cost of this unfortunately, is about $1000-1200.
When the vehicle goes into limp mode, it doesn't tell you. It also may not give you a check engine light. When you say there are no fault codes, what type of scanner are you using? If it is a basic OBD scanner, it will only be able to read the engine fault codes and not of the ETC or ISM modules necessary to diagnose the problem. Its pretty unusual for the transmission to be stuck in a gear and not have any faults stored in the transmission or ISM modules. If you are getting the do not change gears and drive to workshop message, it can be faulty software in the ISM shift module. I would rather have new software tried in the ISM module before I replace it (expensive). Have you tried disconnecting the ground cable on the battery under the passenger front seat to see if it will reset?
Sorry, but good luck. It looks like a tow is unavoidable at this point. The conductor plate or ISM has failed beyond a simple reset.