This is the same thing that has been happening to me.But it has happened enough that I have narrowed it down.
It's at the point where I should be getting my first Hero. When it end my turn and my fame reaches 3.
The only thing I can do is save the game. Exit all the way out (usually with an end task from the task manager) then come back in and reload.
The game starts up fine and continues, but I never get that first hero.
Seems like the window for the selection of the hero is getting hidden behind the main screen or is made active but not made visible. The game is waiting for my selection but i can't make it cause I can't click on anything.
Exiting the game clears the window conflict but I don't get a hero until i can earn 50 fame.
Any info on work-arounds or a way to get the hero selection window back to the front would be appreciated.