http://www.gmpartscheap.com/seccat/cavalier-697/2003/shift-boot-41002/124/
The neutral safety switch, on your 1993 Chevy Cavalier, is located beneath the shifting column. The switch can be accessed by removing the shifting boot.
Not sure on how to replace it, but it is located INSIDE your center console (which will need to be removed if you cant get to it by removing the shift boot) it is a pressure switch at the base of the handle...
Pull up the shift boot, on the right rear of the shifter body is a button that you press in and hold while you shift into gear.
There is a torx screw on the same side as the button, unscrew it half way and lift up the shift with the boot.
* Remove the shift lever knob,console and shift boot * Disconnect the shift and select cables from the shift control assembly * Remove the large shift cable retainer plate and detach the cables from their bracket on the shift control assembly base * Remove the shift control assembly retaining nuts and remove the shift control assembly
Twist boot then pull, this will break the seal from the plug.
Turn it counter-clockwise until it comes off. It is connected to the leather boot by a pressure clip. A little tug should remove it from the boot, but be gentle.
It is located under the shift boot just pull up on the boot. On the 02- early 03s there was a recall if you see a handle call your dealer to see if the recall was performed otherwise to the right of the shifter there is a "button" with a spring. The manual in your glove box also should show this.
use a razor blade and slice a small slit the size of the wire in the rubber boot that the brake cable or throttle cable goes through, it may be easier to put the wire through the steering columb boot. after u put a slit in the rubber boot just push the wire through.
I talked to a rep from GM and he said that the whole shift arm has to be removed down below the boot. I had the same problem in my S-10.
Sounds like your shift interlock mechanism is jammed. Assuming yours has a floor-mounted shifter, there's usually an override button on those, which requires you to pull up the rubber boot around the shift column.
pull the shift boot down. loosen the jam nut under the shift knob then unscrew the shift knob.