For the last few months, when I launch Dragon, Dragon Pad opens (because I've set the Options to do that), but the Dragon Bar does not appear.  To make the Dragon Bar appear, I have to wait until Dragon Pad opens and the user profile loads, and after that I can click the Dragon icon a second time in the Windows task bar.

That's not the way it used to work.  Before, launching Dragon would lead to both Dragon Pad opening AND the Dragon Bar appearing.

Is there a setting I'm missing somewhere that somehow got changed?

Try opening your Dragon Options/Appearance tab, remove the DragonBar checkmark (it looks a little different in DPG 15.6), click the Apply button, put the checkmark that you just removed back followed by clicking the OK button.

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Thanks, but in 15.3 there are only radio buttons.  I can't "unselect" a radio button except by choosing another radio button.

I tried resetting to defaults and choosing other options, each time quitting and relaunching DPI, but nothing worked.  I still can't get the Dragon Bar to show at launch or in any other way except to click the Dragon icon in the task bar again.