Yes, it's definitely an electrical issue somewhere in the theft system. This can include anything from the ignition cylinder, security
sensor or module, or the wiring to those units. Since the theft light did come on, there would have been a trouble code set in the system. This can be retrieved by getting the car scanned for codes.
You might want to take it to a shop or dealer that has a good scanner, as your local auto parts store will not be able to scan the body control systems on your car, but only check for engine codes. I've seen many times where someone takes their vehicle to Autozone or Pep Boys to get a free scan of the car only to have them tell you that you have no codes at all, when you really do.
When you have an issue like you are experiencing with the theft system on your Taurus, your best bet is the dealership.