Have your ball joints checked out.
Accelerator!?
Yes, a broken or disconnected accelerator cable is the likely cause for the accelerator pedal to quit working. The car will still run fine but will not be able to accelerate past idle.
with me it was the o2 censer
Weak fuel pump? Fuel filter? Air filter? Sloppy timing chain Timing not adjusted properly Vacuum advance not working? Accelerator pump in carb not working?
accelerator pump inside the carburator
if it runs fine until you push the gas pedal the accelerator pump may be bad if it has a carb on it.
Low fuel pressure
In my experience with my Chevy it was a ground wire
have you checked your fuses?
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.