2001 Honda Civic Question: Automatic car won't reverse or drive when put into gear.

While driving my automatic, it did not want to go into the next gear as speed increased. Later that night, it would start up but not reverse or drive when put into gears. It would only ease forward as if it were in neutral. I checked the transmission fluid and it was quite low, so I put about 4 quarts of fluid in it. Since it began not reversing or driving, the battery has been dying. What is your professional opinion as to what may be wrong with the car? How much will it cost to repair?