What is your setting under Quiz > Quiz Preferences > Settings > Required?
I have not actually seen this issue before personally.
But try changing Required setting to Optional and then look to see if the button is no longer greyed out when you publish.
If the button is still faded, check if there are any effects applied to the button.
You were right all the time, the quiz settings were causing the "issue". I should have used "Required", instead of "Answer All".