OK it looks like the mystery of this troublesome hive has been solved. I have tried to requeen them and that did not work. (they killed the queen in the cage). Finally took some photos and blew them up on the computer. Multiple eggs, not in the center and not in the bottom of the cell.
Laying worker!!!! So I will be introducing for about 3 weeks, a frame of open brood every week in the hopes they start to understand that they should make a queen.
Wish me luck. Guess I could lose this hive if they do not get it.