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The anti-theft system that is causing the problem is a passive anti theft system. It does not matter how long you disconnect the battery, it will not reset if there is a problem. Now, with that said, my guess is that something different has happened. If, in fact, you lost the key to the vehicle, a dealer would have to reprogram it so the PCM (power control module) and the PATS system recognized each other.
Since you replace the battery terminals, I would suggest checking the main engine fuses located in the power distribution box. I attached two pictures for your review. The first is of the maxi fuses in the vehicle. Note that number 5 is for the ignition. Check to make sure that fuse is clean, tight, and not blown.
Check that and let me know what you find.
Images (Click to enlarge)
Tuesday, June 19th, 2018 AT 8:09 PM