It sounds to me that you don't have a factory keyless entry, but the aftermarket, dealer installed Ford alarm.
If you had factory keyless, your remote would look like this:
-4 buttons
-black unlock button
-black lock button
-red panic button
-blue trunk button
I'm assuming that the dealer installed alarm had the anti-theft cut off hooked up to the fuel pump instead of the starter like it should. I'm also assuming they didn't wire it correctly because if they did, unlocking the car with the key should also disable the anti-theft system. What you need to do is find the alarm brain, find the anti-theft wire, and trace it to where the alarm wire is wired into the fuel pump cut-off switch and find some way to stop the alarm from controlling the fuel pump.
If you aren't comfortable with this, take your car to an electronics shop and ask them to troubleshoot and disable that feature.
