Will not start and anti-theft light stays on

We need to start with checking for codes. More than likely you have a sensor or other issue but it is just a guess at this point. I would think you have a BCM code which will tell us what the theft system is activated for.

Here is a guide that covers the basics but again, more than likely we will need to pull codes if deactivating it doesn't work:

https://www.2carpros.com/articles/how-to-reset-a-security-system

What does the light do while you try to start the car? Does it stay on steady or does it blink?

A common failure in these is the pass-lock sensor located in the ignition switch housing, not the lock cylinder. It is the small part with wires in the picture. However to verify that is the true problem you would want to use a scan tool to watch what the system does as you turn the key in the ignition. The common failure is the sensor but it could be any part of the system. The scan tool would show what each piece is doing and would save you the money of replacing the sensor and keying it's replacement if the problem is one of the other parts.
Replacing the lock assembly requires taking the column apart to access the lock case release but that isn't difficult, you remove the steering column covers and there is a release button you push. However you need to set the pins to match your current keys as well as replacing the sensor if it's the problem.

The light stays on.

Okay, staying on is a sign that it is either the sensor or the module that is the problem. It should store a code to show where the problem is. You will need a good scan tool to read the security system codes and see what it's saying.