I would check to see if there is a fault code for a vehicle speed sensor (VSS), so you need to have the engine control system (known as the OBD2 control system)) module scanned for fault codes to see if the VSS has set a failure code.
with the tailgate fully open remove the plastic trim on the inside the bolts of the wing will be visible remember to unplug the brakelight connection and carefully remove the pipe from the window washer jet
why unplug disconnect alarm ---doing that will not let vehicle start --does vehicle turn over and not start --does it turn over --when tutning key to start what happens ---
Most oil/lube shops use a process of suctioning the old transmission fluid through the fill tube. On older cars, this process can damage the transmission since any metal fragments in the bottom of the transmission pan will be "sucked up" through the system. Since they won't perform the service properly (remove the transmission pan/filter and replace the filter). This is why they referred you to a dealer. Any transmission shop should be able to service your transmission. Best of luck! Greg
Possible reverse light switch problem or relay.The switch is more common to fail. It is located on top of the transmission and the air filter box assembly will usually have to be removes for access to the switch