Will not start

Reconnecting the battery activates the anti-theft system. To turn that off, lock, then unlock either front door with the key.

There are a number of things that can cause engine stalling, but with your additional observations, it sounds like the charging system has stopped working and the electrical system is being run by just the battery. That will last less than an hour, if you are lucky, and less if you need to use the head lights or wipers. Instead of replacing the battery, measure its voltage, then charge it at a low rate for an hour or two with a portable charger. A good, fully-charged battery will measure 12.6 volts. A good but run-down battery will measure closer to 12.2 volts, and will drop a lot more when you turn on the head lights or heater fan. Also be aware that any good battery will read considerably higher than 12.6 volts right after the charger is turned off. That reading is not accurate. Turn the head lights on for about ten seconds to remove the "surface charge" from the battery. (That is the electrons in the acid that have not been absorbed into the plates yet, but that is not important to this sad story). Now the voltage reading will be accurate.

Be aware too that any diagnostic fault codes are erased when the battery is disconnected, so do not draw any conclusions when there are no codes to be read after reconnecting the battery.

I suspect that was code P700. That is in the Engine Computer which is the only computer most code readers can access. Code 700 means there are other fault codes in the Transmission Computer. You need a scanner to access that computer to read the codes.

Your transmission is computer-controlled, and computers do weird things and get confused when system voltage is low. I wouldn't do anything until the charging system is repaired / working. You can do the first part of the testing yourself with an inexpensive digital voltmeter. Measure the battery voltage again, but this time with the engine running. You must find between 13.75 and 14.75 volts. If it is low, we'll need to take a few measurements to diagnose the cause. If it is okay, that only means it's okay to do the rest of the tests, but that requires a professional load tester.