Take your icm to an auto parts store for testing. Make them go through several test cycles as icm is prone to fail when hot.
When putting old icm or new replacement icm back on, make sure you use heat sink compound on it;'s back and on heat sink back, so icm won't burn up quickly.
Might be an idea to test the ignition switch wiring and connectors. We have 96 factory service manual located in 4th gen section. It will have all wiring diagrams. Look for thread titled "GM service manuals"
When your checking the electrical part of ignition switch, located under dash attached to steering column, first check connectors for burnt pins, loose pins, broken pieces.
Then use wiring diagrams to make sure all power inputs to ign sw are good. Then with switch in run position, that all outputs from switch that should be live in run position, are providing battery power.
One last area to check since you have auto trans. Trans electrics get their power from same fuse as coil and icm. If there is a problem, especially an intermittent problem with the trans power wire, connector, solenoids, switches, this can pull down power to your coil and icm causing car to not run or run poorly.