My name isXXXXX am a Land Rover tech.
If all this happened because the battery went dead then all you have to do is clear out the faults in the trans computer and the engine computer. These faults will set due to a dead battery because the computers can not communicate or function properly with the low voltage. This is not uncommon at all. Make sure the battery is charged so it doesn`t happen again and that should do it. Have a great weekend.