1991 Buick Park Avenue won't start

It's not impossible that the second module you got is bad in some way as well. But, it not It sounds like it might be an issue with a FACTORY alarm / security system. When you turn the key is there a Security System light flashing or on steady? If so, your factory security system maybe the cause, and might need to be reset. If the security system light is not flashing and/or on. Then you'll need to check for possible wiring / fuseable link ssues etc. On the passenger side fender next to the battery, back by the cowling, there are grounds and fuses/relays look for any corrosion in either place. If the security system light is not illuminated, it won't be a factory alarm issue unless the bulb is out. You'll need to see if you're getting power to the fuse block / crank relay. If there is no obivious corrosion you will have to test at the crank relay for signal from the ignition switch and power to the starter.

Thank you for the advice, It turns out that the sensor for the resistor in the key was not sensing the proper resistance I had to install a resistor that had the same resistance as the key inline to get the car to start. Thanks for your response and time.