Tonight I finally got around to opening it up to fix these problems. Now the screen sets into the case properly, and I found where I had accidentally unplugged the speaker, and I put the standoff back where it belonged. I had gotten a tip from yohannon about the battery issue, and sure enough I found a loose cable right where he said it would be, and put it back.
Sure enough, the batteries are still not charging. I am trying not to see this as a metaphor for the way my life has been going in the past year.
(Yes, Google turned me down and I am cranky.)