Unhooked battery hooked back up car will not run after starting

corrupted cpu program in the ECM from disconnecting the battery would be a fair comment
use a scan tool to reset the system and to check for other faults

It won't start as long as the security light is on because the fuel pump is not running. You'll have to find out why the security system is malfunctioning first.

Unhook battery, unbolt alternator, unhook alternator, hook back up new alternator, bolt in new alternator, hook battery back up.

I would unhook the battery for about 10 minutes, hook it back up then see what it does, if that doesn't work check battery, or go to owners manual to reset system.

try unhooking battery leave it unhooked 5 min hook it back up

Power drain is never fun to find. The easiest way to track down your draw is to remove the negative battery cable and hook a 12volt test light between the cable and the negative battery post. The test light will light up showing that you have a power draw. I will usually start by unhooking the alternator as it is quite common for the alternator to loose a diode internally making for a dead short, but still able to charge with engine running. Anyway, unhook the alternator and observe the light. Does it get dim or change at all? if so, replace the alternator. If not, hook the alternator back up and move to the under hood power distribution center. Remove one fuse at a time and look at the test light, if you pull a fuse and the light goes out then you have at least narrowed your search down to one circuit. from there look to the owners manual as to what is associated with that fuse circuit and look for your short.

Won Start or won't keep running , Well if it won't start you need to hook thebattery back up. But if it won't stay runnig after youstart it then removed the hot wire ,(your Alternadter is'nt charging )

Hooking up the battery wrong probably shorted out the alternator so that it not charging. The car was running off the battery and discharged it causing the lights to turn off and the car to want to stall. You will need to have the electrical system checked for damage.

Try to check the connection to the terminals for your battery and then you may have to jump start it to give it some juice and then let it run to charge back up since you completely unhooked it.

First check if battery if it is charge and try again ,or use one that have full charge.
If works you alternater is not charging,
Can also check alternater by pulling ground cable off wile car is running and if stops running change you alternater.