Is it possible that I may have installed the incorrect ignition switch?

If it has a factory security system, that could be the problem.

Just to add to this one do you have a test light or multimeter?If so go down to the clutch switch that the clutch pedal pressing on for the car to start.With the car in neutral and the ebrake on with the key in the start position you should have power going into the yellow wire going into that switch.If you do then its not a security issue or ignition switch issue.If you have power then press the clutch switch in now you should have power to the purple wire coming out of that switch with the key in the start position.Let me know what you find.

Hi thanks everyone for your replies. I actually found that if I close both doors, turn the key to the on position, wait for all the beeps & doors to lock... THE FREAKING THING STARTS RIGHT UP!!!! LOL CRAZY! I try to start it before that last beep, it starts to turn but cuts out! Now I gotta invest in another battery! Thanks again!

Sounds like you have a aftermarket alarm and thats causing it to not start.The factory alarm doesnt automaticly lock the doors on the car and do all that stuff your car is doing before it starts.

Yeah I think its a Viper set up actually.

The factory ones are basic you just turn them off and on with the key fob.Glad to hear you got working though.