Dodges don't have a fuel switch like Fords.
My guess is you had some build up either in your fuel pump or fuel filter and it's possible that gunk got knocked loose in the accident. It's clogging up your fuel system when driving. The gunk settles when the car is cool.
Really you need to figure out what you are losing. Either spark or fuel.
When it shuts off, can you restart it right away. Or does it need to set for awhile? If it doesn't start then do this: Turn the key to the "on" position... don't start it. When you turn the key to the on position, you should hear your fuel pump prime. It will be almost a humming sound. If you do not hear this sound, it means the fuel pump is not working. It should always prime.
Sorry but we can give you a 100 reasons why your car turns off. From my experience, I do all my own car repairs, you have to find out the whole fuel or spark. Once you figure that out, then you can narrow it down.
There is simply test to do to find out if you are getting spark but I wouldn't recommend it to someone who isn't comfortable with cars.
Also check your fuses in your fuse box and make sure they are all nice and snug. Could be a lose connection to the alternator and the battery isn't recharging. Do you get any warning lights?