car won't start, think its the ignition switch

I've replaced my starter and my 97 cav still won't start! When I turn it on, all the lights and dings come on, the car clicks and kinda hums but it won't turn over. We've jumped the engine straight from the battery and it started the car for a mere second or two and immediately dies. We know the battery works (we tried jumping it and all that, no go). We know the starter works. We know it's not the neutral safety switch. I'm wondering if it could be the ignition switch? Possibly the alternator? I'm a girl, I know a very limited amount about cars, but I would like to know and I want to know if I could replace/fix the ignition switch myself if thats what it is. Any suggestions?

I Got A 1997 Cavalier 2.2 Auto. To Start The Car You Would Turn The Key Then Under The Dash It Had A Amber Light With A Small Button To Push. It Would Then Start. Problem One Time I Tried To Start Car The Button Got Stuck And The Car Starter Turned Till The NOISE Was Heard Grinding On The Starter, Suddenly A Puff Of Smoke Like Fumes Came Out From The Steering Wheel Colum And I Turned The Key Off To Shut The Ingine Off. Later I Tried Starting It And It Would Not Trun. So I Looked At The Button And It Looked Okay But I Think Its Not Working Anymore. So I Tried Starting The Car Which I Did By Turning The Key On And Used A Scwer Driver Between The Coil And Starter Post. And It Does Start The Car. But I Tired Of Lifting The Hood And Useing A Scwer Driver. What Do I Need To Repair First. That Wont Cost Me Hundreds Of Dollars.

god damn, trying to break in your "shift" key?

well if u want to do it the wrong way, replace the wiring to your amber switch, as well as the switch. as a professional auto tech, I would get it done right, but to be honest, I have a push button starter hooked up in one of my trucks! :)