Two thoughts, I've had this happen to me a few times.
1. On the drivers side door frame there is a black button that can loosen up and cause the alarm not to work. just give it a wiggle and see if it is loose, if it is tighten it up and give it a try.

2.This is a little more involved loosen up the drivers side exterior door handle remove the two nuts under the plastic cover inside the door. Now that it is loose pull it out as far as it will go inside you will see two plastic clips on the door handle linkage pop the two clips off the ends of the linkage, now you can pull the door handle assem. out alittle further on the end of the lock cylinder there is a white clip with wires attached to it. This clip should be firmly attached (one of the clips that goes down the side of the cylinder is broken on mine and it pops off)

Sorry I can't be more detailed but I don't have my car because it is in the body shop, I got slammed in the rear by a Explorer........ not pretty.

Hope this helps.
X2boxers