I have created an application pool called "schoolPool" and assigned it to my web application. Identity for this pool has been set to LocalSystem. When I try to access my database from within the application, i.e. open a SQL connection, I get the following error all the time:
Login failed for user 'NT AUTHORITY\SYSTEM'
I tried to add NT AUTHORITY/SYSTEM to SSMS (SQL Server Management Studio) logins, but it was already a principal, showing the following error:
Allow NT AUTHORITY/SYSTEM to server Role as sysadmin.
I tweaked the application settings a lot, changing the application pool's identity (in Windows 8.1's IIS) to LocalSystem, LocalService, NetworkService, and ApplicationPoolIdentity. However, all of them failed to solve the problem I had logging into my database.
Finally I set the pool identity on LocalSystem and thought why it might be preventing "NT AUTHRITY\SYSTEM" from opening a connection to my database. I opened up SQL Server Management Studio as the user "Administrator" and checked out the Server Roles for NT AUTHORITY\SYSTEM under "logins" section. The default server role for this user was public by default. I also checked sysadmin and refreshed my web application form. This time it was a success. Great job!
Musakkhir's answer of granting sysadmin seems poorly thought out as far as security goes, and Pinal's answer involved giving the unknown process db_owner rights, still almost certainly overkill. I've 'solved' it myself by simply granting "public" rights, which normally just allows CONNECT, but nothing else, even SELECT. If gets rid of the login error and stops flooding the error log, since it now logs in, but whatever unknown process is doing the connecting still can't do anything.
Rerun following query which will assign 'NT SERVICE\MSSQLSERVER' to sysadmin
EXEC master..sp_addsrvrolemember @loginame = N'NT SERVICE\MSSQLSERVER', @rolename = N'sysadmin'