There are many possibilities ranging from a bad shift solenoid, faulty TCM(tranmission control module), failed torque converter clutch solenoid, or internal transmission problem. Since the check engine light did come on, there will be what is called a DTC(diagnostic trouble code) stored in it. This code number will refer to a specific area or part.
If you want to, before taking it to the shop, take it by an Autozone, or other parts store. They will hook a scanner up to your car and read the DTCs for FREE. They will give you the trouble code number and what it refers to. Then you can post that trouble code number here, just by re-opening this question. I can let you know more on the problem and whether this something that can be repaired at home, or needs to go to a shop and what you will be looking at as possibilities of repairing.
DTC P0700 is a diagnostic code to let the person performing the scan know that there are stored codes in the TCM(transmission control module) and that this needs to be scanned for specific trouble code.
Unfortunately, whoever did the scan at Autozone didnt understand this code and that they needed to do a scan of the TCM for transmission trouble codes.
You can either take it back to Autozone for them to scan the TCM ofr stored codes and let me know which ones come up, or go ahead and take to the dealer to have the do diagnostic scan, and when they call you with diagnosis, ask for the specific diagnostic trouble code numbers and let me know. I can then tell you whether what they are recommending to repair is corrrect or not.
Sorry I cant be more specific at this time, but without Autozone having done the entire scanning to retreive the TCM trouble code numbers, this is all I can tell you at this point, but I will continue to help until problem resolved or you are satisfied dealer is being honest with you. This is what I am here for
Ok, here is the definition of that code:
DTC P1776 - solenoid switch valve latched in L/R (low/reverse) position.
Most of the time it is either the solenoid, pressure switch, or wiring short. Most likely, including diagnostic time, you will be looking somewhere between $300-500 parts and labor for repair. Maybe a little more if valve body is bad.