The key alone doesn’t start the car?

Sounds like the switch or the lock cylinder maybe bad, also could you tell us who installed it? Yourself or a shop.

The easiest test would be to place the key in the ignition and see how it responds when you get to the ON/Run position do the dash lights come on? If so try starting the car ( they all should go out, if not usually the switch is bad. It also would be the lock cylinder not pulling the switch all the way to the starting position ( I had a saturn with this issue, but you could start it that way ). Also the switched ignition lead to the remote start module maybe bad. You may have to fish out on line what model the remote unit is and find a wiring diagram and figure out what they did under there, I also have seen in the past where the units are not tied down real well and one good kick under the dash and it messes everything up.

The reason however its still starting is that the remote start box overides the keyed ignition by directly controlling the 12v switched lead running to your starter ( also tied to PCM so it knows weather or not the car actually started, usually by rpms)