No, the airbag circuit has nothing to do with it. There is an inertia fuel cut-off switch on fords that will cut the fuel in the event of an accident, but if it won't even crank then that isn't your problem either. Most likely you jarred something loose in the accident. What year mustang is it?
Ok then you don't have PATS (chip in the key), so thats not why either. Are you just trying to start it to see if it runs still? If thats the case, you can turn the ignition on and jump the starter. If it still doesn't turn then your starter is shot. Also make sure your battery is still good.
Here's a thought, if its an auto, is it in Park? I remember a guy who thought his car was dead after he hit a guard rail and he tried to start it and it wouldn't crank. Turns out he wasn't paying attention and it wasn't in park.