I'm new to Stangs, so I don't know if you have an electric pump, right? I betcha if you disabled the alarm system, you'd still have fuel delivery problems. Sounds like there is a common wire shorting out (possibly the ground).
Separate the variables and chase one problem at a time, rather than assuming that both are directly related. Does it matter that the car doesn't move but the security system works? Fix the fuel delivery first.