This should also solve the issue of "Updating game client..." or whatever it is.. frozen screen before the launcher.
-> Right click Diablo III.exe in your D3 folder and click 'Send to Desktop (shortcut)'.
-> Click Properties
-> Add " -launch" to the end of the field there. An example is below, and also includes the quotations.
"C:\Program Files (x86)\Diablo III\Diablo III.exe" -launch
This will force your shortcut to bypass the launcher and directly launch the game.
I hope this helps.