>But if there were never any eggs or brood, they couldn't have raised a new queen, right? I installed the hive 2 weeks ago, and now there are only workers visible.
Capped worker brood?
> The queen that I installed with them should have started laying by now, and she was presumably not a virgin, was she?
I have gotten packages with virgin queens loose in the package, in which case they usually reject the laying queen. It may be a week or two later before the virgin that came in the package starts to lay. If the laying queen shipped with the package layed any eggs and if the bees made a queen it would only take them 13 days from when they decided and 16 days from when the egg was layed to make a queen. Then two more weeks before that queen would start to lay.
> I thought that the queens sent with packages should be ones that had already taken their mating flight.
Yes they should have been.
If you have a frame with some eggs, I would put that in and see what they do. If they try to raise a queen, then they are queenless. If they don't, then there is probably a virgin that hasn't started to lay yet.