If you open up a command prompt and run the following, what do you get?

setspn -L <domainName>\<accountName>

Where <domainName> is the pre-Windows 2000 naming convention for the domain (ex: Famicam) and <accountName> is the name of the service account that the SQL Server service account is running under (ex: svc.sql.server). So for example one would run:

setspn -L famicam\svc.sql.server

You should get entries back for the MSSQLSvc for your SQL server.

Are connections being made directly from an application to the database, or is there more hops involved? For example like with SSRS, a user hits a report server and then the report server can relay the credentials back to the SQL Server. Just curious because depending on how many hops there are there could be several layers of delegation between different accounts/services that need to be setup.