Hi Paula,
I believe you are correct about the immobilizer acting up. When the control system could not read the transponder it would not allow you to start and that is where you see the security signal staying on or going off. A scan tool should be able to let you know if any error codes had been stored.
I am not sure if scan tools provided by parts stores have this feature but you can give it a try.
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Wednesday, June 20th, 2018 AT 8:24 AM