Do you think this is likely?

What is your question?

We had a front end collision. Our car was hit on the drivers side front corner. Front bumper and headlight messed up. Air bags did not deploy. Other car had only dent in fender. The fluids did come out at accident.....2 colors. The car was towed to our house. My husband tried to start the car. It did start but would not shift into geer. We assumed it was due to lack of transmission fluid. Body shop is telling us transmission is shot. How likely is this? We don't want to be ripped off. No collision insurance and quote for repairs is already $2600.00. Please advise.