You won't see anything in your Dock when you start Edge Inspect.
Instead, you should see a new icon with the letters "In" in your menu bar (top-right of your screen, to the left of the clock).
Do you see this icon?
If so, click on it and you should be able to Sign In (if you're not already). You can then set up the remaining components of Edge Inspect to get started testing your content: http://www.adobe.com/go/edgeinspect_ig
If you do not see this icon, then we may want to check in Console (under /Applications/Utilities) to see if there is a crash or error log.
The menu bar icon flashes for a split second before I can click on it then dissappears.
OK, then please look in the Console for a crash log, and post it here.
Since you mention that the "report crash" process was running, the log you need may be filed under FILES > ~/Library/Logs > Crash Reporter.
If you do not see it there, try looking farther down under /LibraryLogs > Crash Reporter.
Once you find it, either do Edit -> Select All and Edit -> Copy to paste it in your reply, or you can do File -> Save A Copy As to save the .crash file and upload it to file sharing service.
I just tried to launch the app (from Spotlight if that make a difference) and it worked!
But just for you guys, I dug up a log from when it was still crashing (not starting) for no apparent reason. It's in my dropbox below:
Sorry for the long delay.