During setup, when I try to ctrl-drag the toy into the Yellow Setup Ball, I get the little "no-entry" sign, and nothing happens.

First, the most common fixes:
If those didn't work, then we check for a more rare problem:
  1. rightclick the Yellow Setup Ball and choose "Edit".
  2. Look in the "General" tab.
  3. Verify that it says "You cannot modify this object"? (if you can modify it, then please go back to the above fixes)
  4. Rightclick your Command HUD and choose "Edit".
  5. Go to the "Contents" tab and look for the "Happy Setup Ball".
  6. Verify that the permissions (in brackets) include "no modify".
If 4. and 6. verifies that you have no modify rights, it means that the Second Life asset server has messed up the Yellow Ball, even though it was just sitting in your HUD minding its own business. This is a known Second Life issue that happens from time to time.

To fix, you need to get a new set.