Welcome to Just Answer,
Are you having a problem with the shift lever itself not moving, or is the vehicle not moving when it is in reverse?
It sounds like you have a problem withthe shift interlock system. This is what keeps you from moving the shift lever if the brake is not applied.
If you remove the shroud from around the steering column you will see this cable assembly, it has an electrical connector at the end of it. You can manually move the linkage where the cable connects. This will allow you to get the vehicle in gear.
If you can not move the linkage you will have to remove the cable as the solenoid at the end of the cable is stuck. Once you can move that linkage you can get your car in gear and get it to a shop, or if you like I can help you diagnose the problem. You will need some electrical test eqipment to do this.
Here is a an adjustment procedure for the cable:
BTSI FUNCTION CHECK
Good Luck, let me know if you need more info.
Tell the mechanic you are hving a problem with the shift interlock, cost is dependent on the actual time is spent diagnosing the problem. The shift cable itself calls for lessthan an hour to replace, approximately $80 depending on the shops labor rate.