How to install a transmission shift cable in a 2000 Cavalier

sounds like it may be the pin for the shifter came out or it is loose, or possibly the cable or rod came loose or broken. take the covers off the steering wheel lower part plastics to the shift and have a look to see what happened. do not remove any thing that is electric with out disconnecting the batt

There will be a cable running from the lower firewall to the transmission, hooking onto a small lever. They usually use cheap plastic clips to hold the cable in place. Could have come off, so moving the shift lever isn't engaging gears.

1999 cavelier manual trans: My son was shifting his manual trans really rough (ramming through the gears to try to beat someone out at a light) and ended up not being able to put it into anything but 3 and 4 (straight up and down). We noticed that the shifter cable, that actuates the position of the arm on the transmission, had pulled away from a "c" clip and was not held into place about 8-10 inches down the cable away from the trans. The cable needs to be secured into that clip in order to let the wire inside move the trans. lever to shift. Otherwise you will be stuck on what ever "rail" your trans is on at the time of disconnection. It would be the first thing that I would check.

Greetings, sir, W/D here.
Check the transmission fluid level and quality. If the level is low, top it off and retest. If the transmission has many miles on it, have the fluid changed. These are the two most common issues with your problem. A transmission check and tune-up, with new fluid would be my last resort, as I generally do not trust transmission shops. If you have access to the underside of the car, and can provide safeguards to work safely (jack stands, wheel chocks), you can also check for deteriorated vacuum lines and hoses.
Best regards, --W/D--

If it's an automatic transmission....
Try a SMALL amount of light oil on the transmission shift selector on the transmission. (follow the cable in the engine compartment down to the transmission) If its covered in mud and dirt, clean it off with water. Also try oiling the same cable internally.

Foot must be on the brake for it to shift into reverse. There is a sensor attached to the brake pedal. Check and see if it has come loose or moved. There is another wire outside the car underneath the transmission. Make sure it's connected as well.

This concern is normally caused by check balls getting stuck in the spacer plate in the valve body assembly.These components are internal. the spacer plate and gaskets are around 60 dollars and a valve body,if needed, is around 275 dollars. Then about 7 to 8 hours labor to install.The valve body is a maze of veins and the check balls are what controls how the transmission flows through the maze. when they momentarily stick in the damaged spacer plate, the transmission will build up too much pressure and shift hard,Hope this information helps you,
Ken

There is a cable that goes from the transmission to the Throttle.  If this cable is broken you will not shift out of first.
This is for an automatic transmission.

change the fluid and filter in the transmission

check charging system,check elect,conn.at alt.or alt.itself.