You are a quick worker!
The alarm disables the starter only, so if the car does not crank, then
yes, it could be an alarm module issue that is left.
The "runs" with key out, had to have been an ignition switch issue.
Or the key cylinder is soooo worn out, that the key can be removed
while the engine is running (feel for excessive play when the key
is in the ignition cylinder).
The alarm module can be bypassed to eliminate it as the cause of a
"No-Crank" situation.
If you look up behind the dash (from under the fuse box) to where
the headlight switch is, you will see the alarm module there.
Remove both black harness plugs from the module.
On the one harness plug, you will see 2 THICK red wires (one has
a black stripe). Use a jumper wires and bridge the two wires on
the harness plug.
Try to crank the engine now. If it starts, then the alarm module
was preventing you from starting the car.
If it does not crank, then there is something else going on.
I will be heading out for a couple hours. Will follow-up with
you when I get back home.
Thomas
Friday, April 6th, 2012 AT 7:23 PM