Oldsmobile/Buick Repair: 94 Cutlass Supreme will not start, cutlass supreme, cables and wiring

Question
I have a 94 Cutlass supreme that stopped starting up the other day. I was running errands and was on my second stop when it wouldn't start back up. I tried turning the key a few times and it made a clicking sound. This has been happening occasionally for a few weeks, but it has either started right up with the first turn, or after 2 or 3. In the past, when the car does not start after a few turns the clicking sound stops and I pop the hood, play around with the battery cables and wiring, then get it to start by trial and error, I don't know if this is a coincidence or part of the problem... This time the starter clicked a few times then stopped making any sounds, and stayed that way. I tested the starter myself by hooking it up to a charger, it turned over ok. I also had it tested at autozone and the solenoid and motor seem to be working fine. I checked all of the wires going to the starter and solenoid itself with a voltmeter and they are all receiving a current and cannot seem to find a broken fusable link. I didn't look in the steering column though, only under the hood. I noticed that when the key is turned I can hear a faint click noise in the fusebox, I actually replaced that about a year ago, because a connection was broken, all of the fuses and relays in the box seem to be getting power. I also took a look at the ignition switch under the column, I cant see anything visibly wrong and when I push it back and forth I can the lights kick on, the stereo works, the door locks work, the a/c will kick on... but I know that doesn't mean much. The battery also tests out fine, I also tried to jump start the car and that did not work either. Should I try to look in a certain area for a broken fusable link? I checked all of the wiring and cleaned off the connections for the battery, solenoid, and starter. If not is there any way I can determine if the problem is due to a faulty ignition switch or neutral start switch, or anything else? I also noticed that the security light goes on while I try to start the car. This is one light that normally doesn't come on. I'm stuck on this one and hate to waste a bunch of money on stuff I don't need, any advice you could give would be a great help! Thanks a lot

Answer
Yesterday I said that light should come on, but I believe I was mistaken.
I was thinking you were talking about the check engine light, and then I got knocked off line, and couldn't return.
If you have a chip in the key, try a different ignition key.
This article may interest you, in case you ever want to bypass it, and you have this system.

http://jaycorptech.com/tech/passlock.htm

or click on the VATS link, since yours is older than this one is for.

Van