P1610 and P1612 on 2002 Pathfinder

[dsurls]

Hello,
Yesterday I had to replace a bad battery in my 2002 Pathfinder. I installed it and everything was fine. I then was able to start the vehicle a couple of times to move it within my driveway in order to work on another vehicle. However, later this evening, I tried to go somewhere and the vehicle would not start. It cranked, but would not start. I used my OBDII tester and discovered trouble codes P1610 and P1612. I also noticed the Security light on the dash being solid while trying to start the vehicle.
I tried the suggestions I've read on the forums for disconnecting the battery for a few hours, and for trying to reset the keys using the on/off cycle 3 times before trying to restart the engine again. I also tried using my other key. Nothing has worked.
Obviously, those codes seem to indicate a problem with the anti-theft system, but the fact that I was able to start the vehicle 3 times since changing the battery has me puzzled. Why would the NATS system have become engaged?
Can someone provide some help so I can avoid a tow and trip to the dealer??

Thanks!

David