Extremely hard to turn steering wheel. P/S fluid full no visible leaks or damage to the undercarriage. I was stuck in the snow and my car bottomed out and now is extremely hard to turn the wheel and it's acting like it doesn't want to shift amongst other things.
Answer: Does the steering make a load grinding or whining noise when you try to turn it? With the fact that you bottomed out and now do not have power steering and also seems to not want to shift, with other problems as well, it sure sounds like you did some major damage.
It is possible you bent something in the steering like a tie rod or something. Maybe even the frame is bent. These things would not explain that it does not seem to want to shift though.
If you were stuck in the snow and over revved the engine, you may have caused internal transmission damage and this is causing it to not shift.
I wish you would have listed all things wrong with you Dodge Neon. That may have given a clue to what is wrong.
You are going to have to have a mechanic put your car up in the air and check what all has been damaged.