Have you been to CodeAlarm's website?

The CodeAlarm includes Starter Bypass -- which is frankly a problem because
the car itself has Starter Bypass and the two can easily be competing to
control the starter.

Either the car or the CodeAlarm is in a mode where it thinks the car is
supposed to be secure (locked), and the starter is being bypassed as a part
of the theft deterent system. It is difficult, if not impossible, to say
from here which system is keeping your car from starting.

I have a '95 Ford Bronco (For Sale, if anybody is interested ...) that came
with the factory keyless entry/alarm. I was told that the keyless entry was
not also an alarm, so like a moron I went out and bought another alarm
system and had it installed. I bought the CodeAlarm, and the idiot(s) at the
alarm store failed to disconnect the factory system -- this is the part
where your troubles come into focus. Because both systems are active, if my
Bronco is closed and locked via the door lock switch, the Ford System takes
charge of security, and if the truck is opened other than the Ford key fob,
the alarm sounds and the starter is bypassed. If the CodeAlarm key fob is
used to secure the truck, then that system controls security.

I had to carry the Ford keyfob (large and clunky) in the truck, and the
CodeAlarm on my key ring. As long as nobody used the switch on the door to
lock them on exit, the Ford system would not activate. But, if anybody hit
the switch to lock the doors on exit, then the Ford system would activate
automatically, and it HAD to be shut off or the truck would not start (which
is why I carried the Ford key fob inside the truck).

Your car has a factory system that locks the doors and disables the starter,
AND you have the CodeAlarm system. Sorry for using so much paint, but the
picture I'm painting is that the two systems are competing for control of
your car. Of course, this depends on what the installation technician may
have done, and there is no way to tell from here. One of the two systems
thinks your car is under attack, and is being stolen so it has locked down
the starter circuit. Try using the key to unlock the doors and see if this
action shuts off the factory security system.

If your car THINKS it was locked using the key in the door, then it will
still think the car is supposed to be locked. It doesn't matter that you
never use the key ot lock the doors and that you always use the key fob,
your car is confused by having two systems, so you have turn them both off.