firstly The immobiliser on the ignition key is not connected in any way to the remote locking ...
Secondly as you have tried all the keys that leaves the car ... The first thing i would do is fit a new antenna ring around the ignition lock easy and fairly cheap .. see how that goes ..
Secondly you can get repair wires to replace the female terminals in the immobiliser control unit plug socket .. There is sometimes a problem with the connections there .. Both those jobs done at the same time is most likely to fix it . reading the codes would be a guide too .
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 My comments are only based on my opinions and vast experience .
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