2003 Alero wont start.

I have had a problem getting my car to start. I tried replacing the ignition switch, but that wasn't it. Also i tried replacing the safety neutral switch, but that didnt seem to do anything either. However on the safety neutral switch is what i believe to be a bypass button. When i hold that down the car starts no problem but without it being depressed the car wont start. I have also checked the starter, etc. Any ideas? (i could just wire the switch so that i can start it without depressing the clutch, or tape down the bypass depress button, but i would like to fix, fix this)
http://i.imgur.com/QCBAd.jpg <-- this is a link to a picture of the switch that i am talking about. The upper-most point on the switch is the button i am talking about if that helps at all.