Sarah asks, "The new queen seems to not be willing to lay eggs in
the frames where there are dead brood.  Is this usual?  Should I replace
these frames?  What might be the best way to remove the dead bees from the
frames?"

As much as I hate to say it, it sounds as if your new queen might be a dud!
In fact, if she has been in there for 4 weeks or longer, she is a dud!  If
she has only been there for 2-3 weeks, your difficulty may be that between
your dwindling supply of bees (natural death) and the age of the survivors,
the workers are not cleaning the combs for her to lay.

If she has only been there for 2-3 weeks, give the hive at least one full
frame of sealed brood from your other hive.  Don't worry about the
population effect on the strong hive, it will not be noticeable at this time
of year.  As these bees hatch they, together with the bees from your new
queen, will quickly clean out the frames and the queen will lay in them
without hesitation.

If the queen has been in there for 4 weeks or longer, and your combs are
still as you describe them, she is a dud.  I suggest you kill her and put
the boxes over your strong hive, with a single sheet of newspaper between
them.  After two weeks you can then move this box(es), being certain to not
take the queen.  Be certain they have at least one frame of eggs, bringing
one up from the bottom if necessary, and let them raise their own queen.  If
you are not in a good honey flow when you remove the box(es), close up the
entrance with grass to control robbing.

Best of luck,
Lloyd

Lloyd Spear Owner, Ross Rounds(tm).  The finest in comb honey production.
http://www.rossrounds.com