How do I repair the antitheft system after jump starting my 2003 Pontiac Montana?

Do the headlights work? Interior lights? Not enough information. Sounds like a dead battery. Will it jump start? Have you checked the fuses? Could be as simple as a corroded or loose battery connection.

have a load test done on the battery because if there is a dead cell then the good battery will feed the dead battery and you will not have an advantage from a jump battery

is the theft light flashing or on steady at all?
try starting it with a different key and see if that helps.
you can also lock the driver door with the key, wait 5 seconds then unlock it with the key and see if that works.

Do you have a question? Because if it's in the shop, you'll know what wrong as soon as they diagnose it

First, you can't and shouldn't test an alternator by disconnecting the battery cable while the engine is running. You run the risk of cooking the alternator and the computer. Thats how we used to test generators back in the last century.
Is the check engine light on when the engine is running ? Is the battery charge warning light on ?
There should be a fuseable link between the alternator and the battery that could keep the alternator from charging the battery.
The ignition module would have no effect on the charging system.

Typically next to the battery, there will be a terminal looking plug on the shock mount. That is where you will attach the negative for jump starting the vehicle. Basically, you just need to ground out the wire somewhere, so when they built the van, they included a perfect ground.

That'ts the sound of your starter trying to pull enought power to turn the engine over. Sounds like you need to charge or change the battery - have you tried getting a jumpstart? Get a jump and drive over to a shop where they can check your battery and/or your alternator.

the battery will be on the passenger side front of the engine compartment. It is under the fuse block and cross bar.

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

Could be security if changed out your battery. Look in your owners manual for resetting the passlock II.

Hello.
Usually that means that the battery is dieing.
Check to see if its good.
If thats not it was damaged.

Take it to a local repair shop.

Hope it works