Car wont start unless door is open

I think it’s possible that the key switch still has loose contacts inside or something like that.

That is certainly one possibility. I would "rig" whatever, in order to "back probe" connectors while they are connected, clip leads, paper clips, probes, nails, etc etc. Use your imagination. Monitor key points to see what they are doing. Don't overcomplicate There are only so many outputs from the key switch, and if they are not "there" then that is a problem