Would anyone know why your transmission isn't coming out of park and the brake lights wont come on but the parking lights on the back and headlights work on a 96 civic dx?

Look at your brake pedal where it connects under the dash. The problems you are having are both related to the brake pedal. There is a safety feature that won't allow you to shift your tranny until you have applied the brake, and since your brake lights are not coming on, there is either an electrical connection or a mechanical connection that is not working.