Posting for a car out of town. No codes, no money light, battery/alternator test/function correctly. Fluid levels good. Revs fine in park/neutral, place in gear and wont go past 30 km/h. RPM's are indicative of that speed. Place ion reverse and accels correctly. I am thinking TCM but would love your thoughts.

 

I had the same issue today after a released the key a little too quick and missed the start up. The starter just fired but wasn't catching, so I pulled the key, restarted it, and it was stuck in 5th gear. 2000RMP max if I floored it. I found this out by moving the shifter over to the auto shift, the dash showed "5" I parked, shut it off, pulled the key, started it again, and it was like nothing ever happened. Any time something like that happens, I typically think it's a bad ground. Check there first, if that doesn't fix it, find a shop that can scan for transmission codes before you throw a TCM at it. I'm no expert, so hopefully somebody else will come along and give you better info.

 

It went to 5th gear because that is the fail safe for the transmission. Pulling key and restarting forces engine to run it's electronic checks. If all is well, it will clear and start correctly. If issue still exists it will stay in 5th gear until code goes from pending to stored/active.

 

I would do as mentioned and see what gear you are in and if you can manually shift down or up. If stuck in 5th with no CEL, could be either your CSP sensors or your trans. The TCMs don't usually go bad on these cars.