Cannot Login to Fresh Installation of SQL Server 2012

I just deployed a fresh installation of SQL Server 2012 on a Windows Server 2012 Datacenter R2 environment. The installation completed with 0 warnings and 0 failures.

During the installation I specified Integrated Windows Authentication so it did not prompt me for a local SA password. I added the domain security group that should be granted administrative rights as well.

Immediately after the installer completed, I launched SMSS and am greeted by this error when attempting to connect.

After clicking okay and then pressing "Connect" a second time I get this dialog.

The TechNet article relating to this issue says to ensure that Named Pipes is behind TCP/IP in the protocol order, which it is.

Any help would be greatly appreciated.

UPDATE
I tried switching to SQL Authentication mode by launching in Single User Mode, enabling the 'sa' account and setting the password but the errors remain the same.

Yup, that last little comment was it. Even though you can select a domain group for the Instance administrators, it will create this problem. You must add individual user accounts. Thanks for the help and pointers!

In the end I put it into single user mode and ran the following command from an elevated prompt:

sqlcmd -S localhost from the command prompt

EXEC sp_addsrvrolemember
'domain\username', 'sysadmin'; GO

exit

Restarted the SQL services normally and went right in.

StackExchange Database Administrators Q#64100, answer score: 3