Anti theft system light flashing on dash, codes P1610, U1000 and U1001

Just purchased this car. Bought a vehicle specific fitment fuel pump, installed the new fuel pump and tried to start the car after everything was done. Turned out that the battery, installed on 8/2018, was dead because someone had left the dome light on, draining the battery completely. We tried to charge it a bit with a friends van before attempting to jump start it, however no matter how long we let it sit hooked to the running van or tried to start it it would crank and crank but refused to turn over and start up. We had an OBD-II reader with us and hooked it up to see if there were any new codes. The code for the faulty fuel pump we replaced cleared, however we were greeted with three new codes in it's place that wouldn't clear. Those codes are P1610, U1000 and U1001. We have looked them up and have pretty much figured that it's the anti theft system, the light on the dash flashes when attempting to start it, blocking us from being able to get it running. But I am also not 100% convinced that is the full problem because I have been trying to find anyone else who's had those same three codes pop along with the same or similar issues as we've had. The fuel pump is working properly, we checked it out before running the OBD-II reader. Is it as simple as the NATS preventing us to start the car because the battery was allowed to completely die before we changed the old fuel pump with the new one? Please, any information or assistance would be massively appreciated more than you could know because I have been trying to get this dealt with for over a month now because I can't afford to have it towed, let alone towed to a dealership to have them charge me an arm, leg and first born child to diagnose and/or repair or even to reprogram the key and key fob. Thank you so very much in advance for whatever help or information you can provide me with.

Sincerely,
Going Insane in Indiana