For it to be an issue with the anti theft two things would happen. 1) it would crank and crank and crank completely normal and healthy but never start and 2) the green Key emblem in your cluster would be flashing. This would indicate that your Immobilzer unit thinks you are trying to start the car with a non-programmed key.
On to the battery concern. The best indicator is to see if the cluster lights glow as bright as usual when you turn the key on. If they dont, your battery is weak.
Now if they are, and you say you bought a new battery so they should be, your Immobi light (green key) is not flashing, you can hear the fuel pump prime at key on and the car wont start next suspect is the starter.
The best way to check this, without removing it and having it bench checked, is to take a long solid object (long 1/2" extension, pry bar, etc) and bang on the starter while someone tries to start the car. Dont wail on the damn thing but dont just tap it either. If the car starts then your starter is bad. If it STILL wont start then its time to get funky. Start checking/cleaning your grounds, look for any rodent damage to wiring since you said the car has been just sitting, take your starter out and have it tested.
Hope this helps!