wdirons: From Sean's twitter feed it seems like the two most common problems are:
1) People don't already have Visual C++ Redist 2010 installed. (Hello Games and probably steam have released a patch to install this now)
Since I can't post links you have to google "Visual C++ Redist 2010" and download it from Microsoft
2) People don't have their graphic cards updated to the latest drivers.
My game initially wouldn't launch. I temporarily disabled my antivirus (Avast) and ran the Galaxy repair/verify, and the Visual C++ installer popped up on its own as part of the install/patching process. Game is now working fine (outside of not allowing you to alt-tab, which is worked around by running in windowed mode). This is worth a shot if you can't launch the game especially if you run Avast.