Could be the other switch on the tranny, assuming your car is a 5speed and I'm sure it is, if your look under the car (Drivers Side) look up at the tranny and look for a black harness that's connected to you tranny that would be called your "Gear Switch" could be fawked up... and that "Could" be the culprit, unless someone can add some more imput to this..
When you say you put in the new switch... Does that mean there was one in there already and all you did was replace it . If thats the case then make sure the switch is not bypassed some where else . All I can say is trace it down with a test light . If you don't want to deal with it bring it by and I'll help ya with it.
x2 also on what Mineral 02 said... It is possible that the Switch was by-passed maybe not from you but from someone else... there is a way to jump the switch instead of pushing the clutch down, cuz I have done that before when my switch was broken until I replaced it with a new one.
With it open (no switch plugged in) it shouldn't start. It should only start when the switch is plugged in the closed (clutch in) or the AOD jumper is in place.
If you unplug it and it still starts, it's been bypassed elsewhere