Did I get scammed/ripped off?

My girlfriend owns a 2009 Prius which were driving from Boston to Charleston, SC. We're almost home when near Columbia, SC when the dashboard lit up like a Christmas tree and stopped accelerating. We immediately pulled over and I called AAA. We had the car towed to aToyota dealership which was about to close. Rented a hotel room for the night and received a call that it would cost $5000 to $6000 dollars to replace the battery. Then they also suggested that they had a mechanic they could bring in who might be able to look at it and check the cells and replace any individual cell as need be for a fraction of the cost. My girlfriend went to the dealership as it was her car and wanted to go while I stayed with the dogs at the hotel. When she got there the mechanic said he could fix it for $675 but couldn't work on it until he put gas in the car because it was empty(girlfriend said there was no warning beep for the gas but it was low) My girlfriend waited for hours but they couldn't get the gas until a truck came back. She finally left a 1:30, car still not being worked on. She went back at 3:30 because that was the latest time that the dealerships driver could pick her up. When she got there the car was out front and ready to go. She wrote a check to the mechanic and the dealership charged her $12 for gas and gave her a recite only for the gas but told her all the work was garenteed but gave her no warranty or a detailed recite of the work. Were we scammed? Is it possible that they put gas in the car and it started and charged the battery? She has cancelled the check until she gets the proper paperwork.