Won't turn over? You turn the key and nothing happens, the engine doesn't crank? Any click from the starter?
Or
The starter motor turns the engine over but is doesn't start / fire.
The best way to diagnose is to find a local auto electrician. A professional grade scan tool computer can diagnose all the electrical computer systems, modules and sensors.
https://www.google.com/search?q=auto+electrician+near+me
..
Question edited for clarity.
Question moved to model category.
The BCM is located behind the glove box. Open Glove box, empty contents, grab sides of box and push inward a little bit and continue to open door. Once that's done there are 2 modules back there, #1 is ECM #2 is BCM, The BCM has a yellow clip on it.
https://www.google.com/search?q=2013+Ford+Taurus.+Where+is+the+location+of+the+BCM
..
On a 2003 it is likely to be breaks or damage in the wiring harness that goes from the driver door into the door frame. All the wires from the driver door switch go though there. With constant opening and closing the wires can work harden, wires break, resistance increases and they burn out and short.
The wiring can be tested for shorts.
https://www.google.com/search?q=auto+electrician+near+me
..
You need to have a mobile lock smith check it out , before changing the key fob battery did it unlock the vehicle ? Your
actual key doesn't unlock the doors? Replacing the fob battery has nothing to do with it,it doesn't lose it's unique RF signal .
you need a lock smith or depending where you at, tow truck drivers have the tools to open the vehicle,
https://www.startmycar.com > Taurus > Manuals
1999 Ford Taurus owner's manuals ... Looking for another year or model? Let us know! Do you have any PDF manual to share? Upload it and share it.
Question edited for clarity.
Question moved to model category.
The BCM is located behind the glove box. Open Glove box, empty contents, grab sides of box and push inward a little bit and continue to open door. Once that's done there are 2 modules back there, #1 is ECM #2 is BCM, The BCM has a yellow clip on it.
https://www.google.com/search?q=2013+Ford+Taurus.+Where+is+the+location+of+the+BCM
..
Check Fuses and Relays, but this has a GEM (general electronics module). You may need and auto-electrician as nothing covers brake lights, but that may be a fault with the brake light switch.