So if I read all this correctly, after re-attaching my battery. I need to...
Lock, unlock the car then enter the following on the PIN Pad:
* 17856 * 38 #
then the dashboard LED should blink, 1,2,4,8, or 16 times to tell me what is triggering the alarm.
If all of that fails, I need to lock the car manually (without the remote) and see if the alarm still goes off.
If it does, it's a chance that it could be a low voltage issue.