90 Buick Riv - will not start

This is complicated. So, going to Just say what all I did and see if someone knows what is wrong.

The car will not start, Even if you "cheat". Please read below

First, replaced the starter, as when you turn the key to the start postition. It did nothing. After replacement, no change. Next. Using a testlight, I attached that to the wire under the dash that is used when the key is turned to the start postition. Grounded out the light and hi the key, it came on in the start postition. Ignition switch is eleminiated. So, I decided to cheat. Thinking that I got a bum starter. turned the key to on, climbed under the car and jumped the starter. The starter cranked over but, promptly died. It is like it is thinking someone is trying to steal the car. (I really hate this computer stuff.) I dont have a clue what to test next. I do know that the wires from the switch goes to a box under the center console and then goes from it to the ecu. where it goes from there is anyones guess. What I would like to know, is what is that first box and what should I check next?

First post, and not use to computerized cars. So, if I missed something stupid, please, let me know

Edit to add: The engine is a 3.8 if that makes any difference. Don't think it should, but never know

sounds like a sensor somewhere is keeping the car from starting, does it have an alarm system? (pass key entry, where it shuts the car down if the wrong key is used) do the 90 riv's keys have a chip? also there are a couple of sensors that can keep a car from starting like the neutral safety switch on the tranny. maybe one of those sensors is bad/stuck on. is you have an OBD I scanner i would check to see if there is a code. good luck.
matt