1997 Chevrolet Cavalier Auto Transaxel problems Help!?

My wife’s 97 Cavalier has some shifting issues. I am a back yard mechanic but stumped with this one. It will go forward but the motor bogs but it will still drive. It will not shift into reverse and the car cannot be pushed when in any gear including neutral. The breaks are not locked up. When I put it into neutral and rock the car back and fourth I can see the motor moving so it is like the transmission is locked up or something. Are there any sensors or anything like that that will cause the car to appear or act like it is always in park? Any other ideas? We don’t want to put a lot of money into it becuae she is going to buy a new car soon.