Help please, X Type won't start
 

My 2004 3.0 X Type drove normally to the gas station, but would not start afterward. It displayed "Gearbox Fault" and all lights, radio, fan, etc functioned. I drew codes 0753, 0758, 0763, 1745, 1746, 1747 & 1603. With the key on and brake depressed it moves freely between gears and the gear indicators backlight appropriately. I also know it went to neutral, since I had to push it to a parking spot. I swapped batteries with a freshly charged one, and checked the inertia switch on the passenger side panel. My next plan is to check the TCM, but after that info seems to get scarce for this fault and 2004 and newer. With the wiring change there are several tips that don't apply to this car. Thoughts from those experienced are greatly appreciated.

If you had checked the first three codes (I assume you're listing them in the order you read them) relate to the shift solenoid. I'd start there.

Was it raining when you were at the gas station?

No rain before it failed to start.

An update is that after some rapid movement of the shifter I got some new "clicks" under the hood when I turned the key. I decided to repeat that and rapidly, if somewhat aggressively moved the shifter from park to drive and back about a dozen times. Following this it started and was in limp mode. I shut down and was able to restart. This has me out of limp mode, but the shifts were not as smooth as normal. Not to a point that it couldn't be driven, but enough to let me know there is still an issue. Does this still point to the solenoid? I certainly follow that piece to the les then smooth shifts, but does it also address the failure to start?

I have a manual trans, but over the years auto trans cars seem to have had trans problems. The TCM is in the drivers footwell and the connectors seems to be a problem, often due to water getting in. The solenoids (3 in total) are in the trans and are directly connected to and controlled by the TCM so a bad connection could be the problem.