My immobilizer light stays on

The security light coming on and staying on means there is a component failure in the security system. A scan tool that can talk to the security system should be able to pull a code to at least give an idea as to the part that has failed. Because it stays on it isn't a bad key. It could be a bad switch or the module itself. The code should point the way.

Correct. A dealer level scan tool is about the only item that can talk to the system and find out what is and isn't working. If the light was flashing when you tried to start it then it is a key recognition problem. As you say it stays on and the other lights don't come on it is a hardware failure.

Sorry to hear that, but it's your choice. You might want to call a few shops to see if they have a scan tool that would work.
This is one of the biggest issues with the modern security systems on these vehicles, they are not something that is easy to diagnose or repair unless you have a top end scan tool. I can understand the factories not wanting an easy vehicle to steal, but they could make it easier for the owner to at least be able to tell what is wrong. However they are rapidly going the opposite way in many brands, they want to limit any repairs outside a dealer.

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