It could be starter, battery, keyswitch, neutral lockout switch or electrical connections.
wires on the starter are criss crossed
more than likely it is your starter telling you "hey bud, yeah its time" My 99 was doing the same thing. Turned out to be a bad starter. Replaced it and took some pics along the way. You can see them at the following link. http://hubpages.com/hub/Starter-Removal-1999-Pontiac-Grand-Prix
Try moving the tube in the fittings, if this doesnt work, then you probably need a new starter motor.
If the engine won't turn over when you operate the key that's a pretty good idea. You then check battery condition and connections first. If they are good, then go to the starter and check for good grounding and voltage when the key is turned.
Probably the starter, have someone turn the key to the crank position while you gently tap the starter with a hammer or bar. If it starts change the starter. If not try shorting the starter solenoid to see if that works.
right after I turned the key
Besides the smart alec answer "start an automobile", a starter has a small gear, that will both extend as well as rotate when the key is turned. This gear will engage teeth on the flywheel/flexplate, which is bolted to the rear of the crankshaft. As the starter turns, the engine will be turned.
A 1986 Ford F150 starter won't stuff off when the key is turned off if the ignition switch is jammed. This will cause the start signal to be sent to the starter continuously.
The starter relay feeds power to the starter when the switch is turned to start. The relay will be mounted either on the fender or on the firewall.
Absolutely not. The starter gear must fully disengage the flywheel gears when you release the starter. Otherwise when the engine starts the starter will continue to be turned by the engine.
If there is complete silence when the key is turned, try tapping the solenoid on the starter with a hammer. Don't laugh. I have found this to be the solution in several cases. This is sure proof that the starter solenoid is the problem. You will want to install a new starter which comes with a new solenoid before you get stranded.
The pulser in the tank on Fiero does not exsist. The item that buzzes inside the tank for a second every time the key is turned on is the fuel pump. The computer turns it on when the key is turned on and while the starter is turning the engine. The pump is run by a relay and the oil pressure switch going down the road.