A frame of brood from another hive will give you a lot of answers. If the hive has a laying worker, they will usually create a queen cell at some point of installing a 3rd frame of brood. Put in one, let it hatch, etc. If a laying worker, the bees should start a queen cell on frame 2 or 3. If you have an idle queen, she should start up after frame 1 or 2, and a drone laying queen should be superceded within that time frame. If, after putting in 3 frames of brood over 3-4 weeks you still have a problem then we can get serious about percise courses of action.