This just happened to me 2 hours ago. My 2004 crossfire would not recognize my fob. So like everyone else I used my actual key. When I opened the door the alarm went off. Called AAA to figure it out. They tried to jump me which didn't work. Then he used the actual key to lock and unlock the door several times in a row which helped disable the alarm. Still did not start up. Then he detached the + from the battery for a few minutes. This did set the alarm off again, but when he reattached the + then jumped it again it started up like a champ!! Key fob worked and everything!!
My assessment is that once the car goes into alarm mode and doesn't recognize the fob then you have to reset the system to recalibrate the alarm and the fob. So if this happens to anyone else, detach the + from the battery for 5 min, then reattach, jump and everything should work itself out! Hope this info helps!!