Can only offer advice how to do it for Windows 7 users however I'm sure it's fairly similar for all Windows based OS.
Under "user accounts and family safety" click "Add or Remove User Accounts"
Create a new account (it's located below the different choices available)
Choose a name and make sure to check the Administrator box
Now logoff of your current user account by pressing the arrow button to the right of shutdown.
Login to your newly created account
Load up Diablo 3 and login (it should let you in now)
Close Diablo 3 and login to your main user account
Load Diablo 3 and hopefully problems solved.
Good Luck, this worked for me specifically with the 315300 error and another error I got when trying to login to a different region version.