Jaguar Repair Problems? Ask a Jaguar Repairs Expert.
Right now the engine is cranking but not starting and is the cause of the battery running down?
OK P1397 is for the variable timing and P1643 is a network fault. Neither one should cause the engine to crank but not start. Since you also have a misfire I wonder if the timing has jumped. Sometimes the secondary tensioners fail causing the secondary chain to jump and even break. The only way to check this would be to remove the valve covers to inspect. Of course it can be another fault like a weak fuel pump or clogged filter. We would need to check fuel pressure at the injector rail with a gauge to verify all with the fuel system is ok. Let me know.
Ok P1637 is also a CAN network code. See if the engine will start in neutral. Also try spraying some carb cleaner into the air intake to see if the engine will start and run on the spray.