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The same release pin that stopped the switch from coming out now needs to be pressed in so you can slide the switch into place inside the ignition module. Just press it down with your thumb. Hold the release pin in until you have the switch inserted. Some switches have an angled release pin that you don't have to press down as you slide the switch in. The new or rebuilt switch should slide easily back into its hole on the steering column. Align the shape of the cylinder and the location of the release pin with the coinciding grooves in the ignition module. Keep pressing it in until you hear the click of the release pin setting into place inside the steering column. If you don't hear a click from the release pin, the ignition switch isn't properly seated yet. You may need to push in on the switch a little to make it click into place. It's best to test the switch before you completely reassemble the dashboard, just in case there's an issue. Reconnect the cable to the negative (-) terminal on the battery, then insert the key into the ignition and turn it to start the vehicle. The vehicle should start without any issue. If it doesn't, remove the ignition switch and reinstall it. Now that you know the new ignition switch works, you can set about re-assembling your interior. Remove the cable from the negative terminal on the battery for safety while you work. Dashboards are notorious for the use of overlapping plastic. Start by installing the last parts your removed and go backwards from there. Every vehicle's interior goes together differently, so the order you install the parts will vary from application to application. If you find yourself having trouble getting the pieces to fit back together properly, refer to a vehicle specific repair manual for help. Be sure to use either the screws or clips to secure each piece as you go. Don't force trim pieces together or they may break. If someone won't go on properly, take it out and look things over to see what's stopping it from seating properly. With the dashboard completely assembled and the new ignition switch working, reconnect the cable to the negative (-) terminal on the battery and tighten it with the right sized wrench. Make sure the cable is secure and can't jiggle loose.
Squeeze the release pin on the ignition switch so it's flush with the side. Slide the ignition switch into its hole. Reconnect the battery and test the new switch. Shut the engine off (if it starts) and disconnect the battery again. Put the dash back together in the opposite order of how it came apart. Reconnect the battery.