Welcome Aboard!
The security system used on a '98 Cavalier is called Passlock. There is a magnet in the key lock cylinder which rotates past a sensor in the switch mechanism. If a thief forces the lock the key cylinder is not turned, the magnet does not pass the sensor, and the system will disable the engine (fuel injectors) after about two seconds.
If it has not already been done, the ignition cylinder sensor from the new steering column will have to be "learned" by the PCM and security system. It will take about half an hour to perform this.
Make sure the vehicle battery is fully charged. Insert the ignition key and turn it to the RUN position (not START) and monitor the SECUITY warning lamp. The lamp should flash if the security system has not learned the new switch. Keep the ignition switch in the RUN position for a minimum of ten full minutes - The system will be monitoring this length of time, so it cannot be shortened. After ten minutes the SECURITY warning should be off or on fully (not flashing). Without starting the engine, turn the ignition switch off and remove the key.
Re-insert the key and turn the switch to the RUN position again. Monitor the SECURITY light again. Keep it in this position for another ten minute minimum period. Again, turn the ignition OFF and remove the key.
Again, and for the third time, insert the key and turn the switch to the RUN position. Keep it in this position for another ten minute minimum. Again, turn the ignition OFF and remove the key.
This should complete the re-learning of the ignition cylinder and sensor to the security system. If so, the next time the ignition key is inserted the SECURITY warning lamp should turn on briefly, then off (bulb test). This is the normal operation of the system. The engine should start and run normally after that.
Please report results.