And all the problems I've been having with that setup.

Well, about a month ago my hive had a swarm.
We saw it leave, but couldn't find it.
I checked the hive about 10 days later.
The bees were very busy and I thought I saw a few eggs. Maybe only about 5---but only one in each cell.
I did not see a queen.
Since then I've left them alone, but today I thought I'd better check again to see if there was any action.
I have four boxes---mediums.
The top one which was one that I put on just before the swarm is still very empty.
The next to top one is full to the brim with honey. Only honey. No brood or eggs or anything. But beautiful, beautiful honey.
I didn't go any lower because this is the box that has the long (five) nuke frames and I didn't want to bust them up like what happens every time I move them because they have all that comb beneath.
So...I don't know what's happening in the bottom two boxes.
Could there be a queen there? Probably not, right?
So, what should I do? Should I go ahead and check in the bottom boxes for brood, etc. Or should I assume there is none and get another queen?
Or is it too late for a queen?
Should I just start over next year?

If it's too late for a queen, should I take that honey. Are the bees going to die anyway?

What should I do?