Looking for help!
My son and I have tried to start a new hive this spring.  we ordered new equipment and 2 lbs. of bees and a queen.  Here's what happened:
1.  we put the bees in the hive with new queen in the little cage.  after 3 days I checked and there had been no effort to get her out, so I decided to help them by opening the screen a little and the queen flew out.  I didn't know if she went back in or not.
2.  I waited several days to see what would happen.  I didn't see any action other than the bees were busy.  I ordered a new queen. by the time she got here it had been 3-4 weeks. When I opened the hive there were lots of capped drone cells but no others.  A local beekeeper said I probably had an unfertilized queen or maybe a worker laying.  this queen was almost dead when I got her so the supplier sent me another one. 
3.  I put her in the hive in the cage and in a few days she was out of the cage.  a week later I checked and there were some cells in almost all stages but not very many.
4  this is now a week later and I checked them again and there are just a small number of capped normal cells in the lower area of a couple of the middle frames.  I had expected to see a much larger brood area than this by now.  there is still a good size number of bees after 6-8 weeks of their arrival here.

what's happening and what should I do to get this hive in gear?  Thanks, Steve