1999 Civic EX, Starting Trouble

I just recently bought a 1999 Civic Ex. It’s a great car. However I have run into one problem: the car will only start if I use the remote entry system to unlock the doors. If I use the actual key to unlock the car, when I go to start the car, the engine will not turn over. The radio, lights, etc will work, but the engine will not start. The only the way the car will start is if I use the remote to unlock the car.

Does anyone know why this would happen? Is it a safety feature of the cars’ alarm system?