Cannot Login to Fresh Installation of SQL Server 2012
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.