I had this happen once, back when I had a Fiero with an auto transmission. I went out to the car to start it, and nothing... not even a click from the starter solenoid. I went through the whole starting system. The battery was fully charged, connections were good, starter worked when the solenoid was shorted with a screwdriver, etc.
Then I got out the manual and looked at the electrical schematics. I noticed a connection on the transmission for the park/neutral safety switch wiring. So I went and checked that. The plastic tab that held the electrical plug in place had broken, and it worked loose. After I shoved the plug back in, the car fired right up.
The electrical plug I'm talking about is a big wide plug on top of the transmission, next to where the shifter cable attaches. If you want to bypass the park/neutral switch, you can run a jumper between the big purple wire and the big yellow wire on this electrical plug. Don't just use a paperclip. The solenoid draws too much current. It'll probably melt the paperclip.
Also, FYI the park/neutral safety switch is actually on the transmission (It also doubles as the backup light switch). That's why the wiring goes to the transmission. The switch in the steering column is the steering interlock. It locks the shifter in Park when the steering wheel is locked. It doesn't affect the starter.
[This message has been edited by Blacktree (edited 07-13-2015).]