(If you're not very computer savvy and are not comfortable with editing the registry, down below is a script you can use to automate steps 1 and 2.)
1) Open "Regedit" (Hit Windows Key + R -> type "regedit" and hit enter) and delete these keys:
"\HKEY_CURRENT_USER\Software\Blizzard Entertainment\Diablo III Launcher"
2) Delete this folder: "C:\ProgramData\Battle.net\"
3) You'll need to Re-downloaded the client installer from the battle.net account page by going to battle.net -> Account -> Summary -> Click "Diablo III" under "Your Game Accounts" -> On that next page, click "Download Game Client". -> Input your birthdate and download the" Full Game Client". It should be something like "Diablo-III-setup-enUS.exe", (last bit varies by region)
4) Run the installer you downloaded, at the top you'll see the installation path, if that path is not already your Diablo 3 installation path (Typically in "C:\Program Files\Diablo III\"), then click "Browse" and aim it at the directory that contains the Diablo III folder, the installer will append "\Diablo III\" to the path automatically.
Let the installer complete, it's not going to re-download the game entirely, just the bits for the latest patch, and it will restore all necessary files and registry entries. After which your game should be working again.
I was able to launch and play after the patching bug, and luckily I didn't catch the "Starter Edition" bug like a bunch of other digital copy holders did. So, yay! Goodluck, hope this fixes it for you guys too. If it worked for you, leave a comment, request a sticky, help spread the fix to all the other unfortunate patchers!
(Copy the below script and paste into notepad, then go to File -> Save As -> set the "Save as type" to "All Files" -> Then save the file as "fixd3.bat". After that, find the file and Right Click -> Run as Administrator)
echo Removing the Registry keys...
reg delete "HKCU\Software\Blizzard Entertainment\Battle.net" /f
reg delete "HKCU\Software\Blizzard Entertainment\3" /f
reg delete "HKCU\Software\Blizzard Entertainment\Launcher" /f
reg delete "HKCU\Software\Blizzard Entertainment\Diablo III Launcher" /f
echo Removing the Battle.net folder...
rd /q "%programdata%\Battle.net"
echo Now run the Diablo 3 installer to install into the same directory the game is already installed under.