Starter Motor will not turn off

The starter motor would not disengage even when key is off also it will not disengage when the motor is running. Replaced the starter and that did not fix the problem. Any ideas on what we should look at next? Someone suggested replacing the coil pack and some one else thinks it is a sensor or a starter relay. The car is a 1997 Chevy Cavalier 151,000 miles 2 wheel drive automatic. 2.2 liter engine.
Thanks,
Tova