Popular fault with the P38.
The BECM looses sync with the engine ECU so the immobiliser can't be switched off.
Search for "BECM loss of sync" on here, covered many many many many times. You can buy a cheap(ish) tool to fix it called a syncmate. Small enough to keep in your glove compartment and will save you calling out assistance in the future.....but I'd get a Nanocom (a small Range Rover diagnostic computer) because it does other useful things like reading fault codes should you find yourself in the unlikely position of having another problem with your car!
Low battery volts does seem to be a causing factor. Winter is coming, buy a new
one of these now!