1996 Dodge Neon Brake Lights Will Not Work

I have recently bought a 1996 Dodge Neon SOHC automatic, and cannot seem to get the brake lights to work. The brake light switch has been replaced and the light bulbs and fuses have been checked. The parts store suggested replacing the turn signal switch and/or the ignition switch. The ignition works, but when you turn off the car the engine runs until you pull the key out.

Any suggestions would be appreciated.