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Check the battery voltage with a battery tester. If it fails the test, replace it.
Otherwise, disconnect the battery. Touch the terminals to each other for a few seconds, then let them sit for 20 minutes for all power to be drained from the various electronic and electrical components. Fully charge the battery, then connect it and try it again. If it still doesn't work, see if you can get scan codes from the OBDII port with a scanner. If you have one that can talk to the Land Rover modules, even better. If you have codes, post them here.
It takes a few seconds for the system check in progress to complete. More than that and there is a fault in the diagnostics.
Battery is new and has been tested. I left terminals disconnected touching for over an hour. Tried what you mentioned above as well, no codes. Vehicle still will not crank and is displaying system check in process, then everything starts but the vehicle. Changed battery in fob as well.
The battery in the FOB has nothing to do with this, it just serves to power the FOB controls to lock/unlock the car, etc.
Looking further into the service manual, the system check referenced is actually an internal check of the instrument cluster. The only other instance I could find of this problem required a replacement of the instrument cluster, with the associated reprogramming. Perhaps moisture, internal contacts corrosion? Who knows.
A shot in the dark since this maybe instrument cluster related. In the passenger footwell there is a module with three major junctions. I would carefully pull back the carpeting and make sure that the three connectors are seated and secure.