So I've played Skyrim, according to Betheda time about 800 hrs. I'm retired and have added mods, deleted mods, had problems with mods, just decided to start over and in this case I start somewhere else or let the main quest go for a while. I have just about all achievements except for a few which I will eventually get. But this time I decided to start over and instead of being a male I decided to play as a female. I'm guessing this is the wrong gender as far as Skyrim is concerned and our hero. For some unknown reason Hadvar will not proceed past letting me put on my armor in Helgen. He stops prior to going down the hall in the keep to face the Stormclokes. And no matter what I do he just stands there. I even went down and opened the gate and went inside and the only reaction I get from the Stormclokes is one of them saying "You shouldn't have come here", no fighting or anything. I haven't gone past this part because you need Hadvar. I realize that our hero is supposed to be male but if that the case then why be able to create a female character or am I missing something? If this has been posted before, I appologize for the duplication.
I had something similar happening, with both Hadvar and Ralof. When I would get to the first storeroom (where the game teaches you to search through barrels, and you find your first potions), the bad guys would not be there to fight, and I would never get the quest prompts to do the barrel searching. Hadvar/Ralof would just stand at the end of the room, and would only make generic responses when I tried talking to them. I could go on and fight through the rest of the dungeon on my own however (at least the next few rooms, I never tried doing the entire thing). This happened with every new game I started, until I finally deleted the game and reinstalled. It does not sound like the exact same issue you are having. But I mention it so that you know you are not alone in experiencing odd bugs related to the game's tutorial. I do not think your problem is because of a female character. It is just the game acting weird.