I give up. What model year Mustang are we dealing with? Important information as the anti-theft system (PATS) is different between 96-98 and 99-04.
What is the theft light doing?
Assuming that all fuses have been checked are are good. Frist try locking/unlocking the driver's door with the key. If the FOB works, lock/unlock the doors with the remote FOB as well.
Now remove the key from any key rings and just use the key in the ignition. Turn the key on but do NOT crank. Does the theft light go out after a 3 second "prove out"? If not, STOP and find out why. The car will never start.
Attempt to crank the engine. Does the theft light blink during cranking? If so, STOP and find out why. The car will never start.
It may also help to test with a spare key if you have one.
>> P1260 - Theft Detected - Vehicle Immobilized
Indicates that the passive anti-theft system (PATS) has determined a theft condition existed and the engine is disabled. This DTC is a good indicator to check the PATS for DTCs.