Why can't I open Dropbox via Launchpad?
Dropbox has no "Window" to speak of. Everything it does takes place either:


On Dropbox.com
Via the Finder in the configured Dropbox folder (NB: right click a file in the Dropbox folder), simply named 'Dropbox' in your home directory by default. Or;
In the MenuBar




Per Dropbox's Documentation, the primary states will be a blue icon with circular arrows indicating a file is synchronizing, or the green checkmark icon like above, indicating everything is up to date.