ECU swap

Sorry to say that won't work. The parts would likely interchange but those are not the only parts that have to match for the NATS system to disable and work. What is the issue with the system on the 1999?

The 1999 is in excellent shape. It just won't start because the lady that owned it before me lost the keys, then when she bought a new key, it was cut wrong or something. It'll crank all day, but will not start. I have a new ignition switch and key cylinder with keys. Do I have to buy a new ECU?

If it's in good shape and the only thing wrong was the lost keys, use the VIN number to order a set of keys through a locksmith or the dealer. Then have those programmed into the system. No ECU or anything else needs to be changed. When the replacement keys are added in the old keys can all be erased so that none of those will start the car again. There is a way to add new keys into the system but you need at least 2 good working keys to use it. If the lock cylinder has been damaged then you can do the same process but have the new cylinder keyed to match the keys that come from the VIN. If you opt to go with all different keys then you will likely need to change anything that takes a key just to be able to use things like the door or trunk locks.