When you say vehicle will not start does it do anthing when you turn the key to the start position? In other words does the starter spin the engine over or does it just do nothing?
What is the anti-theft light do when it does this? It should come on solid for a couple of seconds then turn off.If it does not see the computer chip in your key it will flash rapidly and block out the starter so it will do nothing.
If the anti-theft system is kicking in then it may be a bad switch on the door lock.The anti-theft looks for the unlock signal to disarm the anit-theft.The problem may be that the switch is going bad on the drivers door lock and when you unlock it with the remote it may not move far enough to make contact so a signal does not get to the module. Then when you open the door the anti-theft sees the door ajar signal but not the unarm signal so it disables the car. Usually this will set off the horn though andd the lights flashing.
The best way to tell if you have a problem in the anti-theft or the PATS system is to watch the anti-theft light. Turn the key to the on position before trying to start it and see if the light comes on solid for a couple of seconds then turns off. If it does then the anti-theft and PATS system is not causing the problem.If it starts flashing rapidly then this is the problem.
If it starts flashing rapidly and the car does not start and you then open the door and take the key and lock then unlock the door and this cures the problem then the switch on the lock cylinder inside the door is the problem.