One thing to try before anything else is to switch on the ignition(engine not running), press the throttle pedal to the floor - switch off ignition - release the throttle pedal - turn ignition back on. Leave it switched on for ten or fifthteen minutes to allow the cars electronics to cycle. After this try starting the car. If it still will not start then you are looking at a problem with either the chip in the cars key, the antenna/wiring in the steering coluum, or the cars ECU. This will require a full scan to find it out.

Maybe when you remove cluster ,you pill little hard harness and pull wires from key reader. They where in but not all the way. Because that wires from key reader goes in cluster harness.

Your immo doesnt change unless you change hw or reprogram it. Your fault says the pick up coil. It may be a loose or unplugged connector. It is attached on the ignition switch. I helped a dead car on the highway the other day that just needed plug wiggled. Weak batteries also can kick in the immo lockout. It times out for max 255 min or 4hours. Let car sit with battery charger with ignition on to time out. You can also check instruments field 22 or 24 (I forget) and it tells you the lockout minutes. Call me if you like. I'm still on the road though.