As a point of clarification, does Firefox launch if you double click it from your Applications folder through the desktop (Finder)? If yes, right click (or Ctrl-click) on the Firefox icon in your Dock and choose Remove From Dock, then drag it on again from your Applications folder. The only other thing I can think is if it's already running but with its window hidden, clicking it again in the Dock might not be bringing it up. In that case try a Force Quit (from the Apple menu at top-left of your screen, click Force Quit..., choose Firefox in the list and click the Force Quit button).