usually bad engine mounts
This happened to me once,but I'm not sure if this is your fix. I left the IAT Sensor(intake ait temperature sensor) unpluged by accident.It gave me whiplash everytime it shifted gears. I pluged it back in and it smothed out. It is in between the air filter box and throtal body.On that big black tube,it has 2 wires. OR,,Borrow someone's tube and see if that does any good. Also put some LUCAS Transmission lube in it. Shifting solenoids may be sticking.
with me it was the o2 censer
Low fuel pressure
In my experience with my Chevy it was a ground wire
have you checked your fuses?
What huh?
Bad heater core.
The 2005 Cavalier could have a fuel leak. Have the entire fuel system checked, as a fuel leak can cause a dangerous fire.
There are several things that can cause your 1995 Chevy Cavalier transmission not to go into drive or reverse. The most common cause is a lack of transmission fluid. A broken shifting fork will also cause the problem.
Dead battery
bad o-rings or not seated and tightened down properly
Blown Head Gasket or Bad Cylinder Head
The 1997 Cavalier has two motor mounts, as well as a transmission mount. If the mounts are broken the motor can move around and cause damage to components under the hood.