That's not a minidump.  Just because the game is frozen doesn't mean it's crashed.  Mine does similar and stays at a blank black screen, even reports as not responding to windows for as much as a minute.  Then it finishes doing whatever it was doing and plays just fine.

In the end though you could always uninstall, reinstall, and redo the updates.

Well, if reinstalling didn't fix it, then you've got an issue with a driver on your system, something on your system is preventing the game from running normally, or you don't meet the minimum requirements.  Check to make sure your video and sound drivers are up to date and reduce the settings you're using in game.  How to do that when you can't get in you ask?  Go to your user setting file and change the values manually.  It's located here:

(On a Vista PC)

C:\Users\(your User Name)\AppData\Local\Ironclad Games\Sins of a Solar Empire\Setting

Some files may be hidden so typing the folder location into the system browser works best.

If you're using just plain Sins you want the User.setting file, if you have diplomacy, you want the diplomacy.user.setting file.  You'll want to play with these options:

VideoAdapterOrdinal 0
VideoIsWindowed TRUE  <- So you can see what's going on with your system without everything going black.
VideoRefreshRate 60
VideoFullScreenWidth 1024
VideoFullScreenHeight 768
VideoWindowedWidth 1024
VideoWindowedHeight 768
VideoMultiSampleType 2
TextureCompressionEnabled TRUE
TextureQualityForShipColor 3
TextureQualityForShipData 2
TextureQualityForShipBump 0
TextureQualityForModuleColor 3    For this group 0 is low, 3 is highest.
TextureQualityForModuleData 2
TextureQualityForModuleBump 0
TextureQualityForPlanetColor 3

ShowIntroMovies FALSE
ShowOpeningCinematic FALSE    Change both to false to disable the videos that play when you first start up the game to eliminate them from the equation.

There are other little settings you can play with in there too...