There is of course another possibility. Maybe the Old Gods are like Avvar gods.
It would make sense, given what we know. Maybe the Old Gods were extraordinarily powerful and ancient spirits that got called into dragons like Hakkon was. If that's the case, then dialogue in Jaws of Hakkon tells us what happens to a "dead" Avvar god - with worship, and sacrifice, a new spirit rises to take the place of the old, becoming what it was.
In his personal quest, Solas confirms that this is how spirits work in general. He says after "All New, Faded for Her" that some new spirit may someday rise in place of his friend, though she would likely not remember him.
This puts the popular theory that the old gods intended the blight and intended corruption in a new light. Maybe they wanted to die so they could be reborn out of their prisons...?
It also means that all the old gods could be running around Thedas already, keeping quiet and biding their time, if all of them had secret worshippers who were preparing the way for them.
EDIT: Also, it would be very funny if the final "push" Dumat needed to be reborn was Hawke praying at his altar. Then Hawke could have potentially been responsible for red lyrium coming to the surface, the explosion at the chantry, the return of Dumat, and the release of Corypheus. Will Hawke be remembered as history's greatest monster? 