2007 Buick Lacrosse will not crank (mimics a dead battery), but the horn blows at each attempt to crank the car. Am told it is the anti theft device that is causing the problem. How do I fix it?

I'm gonna have to disagree on the anti-theft. In most cases the vehicle WILL turn over but will not start because the anti-theft shuts off ignition spark and fuel. If you are not getting anything at all I would start by looking at the starter. Now there is a fuse for the starter you can check. That fuse is located in the fuse panel under the hood of the car on the passenger side of the vehicle. Below is a diagram of the fuse layout. The fuse you will want to check will be the fuse in the number 33 position and is what they call a "J" type fuse. If that is blown you may have a short in that circuit or the starter itselff may be bad and causing it to blow. Just for your information, even if the lights and horn work that doesn't mean that your battery isn't low. It takes quite a few amps to make the starter move and if you are low on power the starter will not work but in most cases you would at least hear a click. If your not hearing anything at all I would start with the fuse and go from there. I hope this helps and good luck.