Car wont start unless door is open

I doubt it, but you need the column grounded if nothing else, for the horn button. If you have a column automatic, the quadrant indicator lamp needs a ground. Not sure what else. The column is normally mounted by sliding plastic/ nylon hardware, which does not lend to ground. The clamp at the floor can be rusty or loose, so that is no guarantee.

So far as the switch, make sure you check continuity and function and make certain of wire colors WHICH MAY BE DIFFERENT on replacement switches.