I don't know if (all of) this is common knowledge but I'll just lave it here. Also, I'll say from start that uninstalling mods is not something you should do in Skyrim.
Most people probably know already that startquest console command won't properly fill quest aliases at quest startup.
What I just found out is:
1. that using stopquest from console before a so called "clean save" will make a start enabled quest not to start if you reinstall or install an update of that mod after the clean save (another thing persisting in the save it seems)
2. if using startquest from console then if some aliases will be filled then those aliases will be cleared again if you load a save.
So, startquest from comsole is not safe even for a quest with no aliases needed to be filled at starup and don't follow an uninstall procedure that suggests a stopquest command if you think you may want to install that or an update of that mod again.
If you bugged your game already like this and you really need to force a quest to start without touching the mod it is in, you could try: (Game.getFormFromFile([that_quest_id],[that_mod_file]) as Quest).start() Make a little esp with a new quest (start enabled) and place that in it's onInit() event, sstart game, load bugged save, save, quit game, remove that esp, continue from the new save.