Ok that tells me that the account that is trying to access the SQL is from an AD domain that is different than the one that SQL is in AND that the AD domain SQL is on does not trust the one being used. Which I'm guessing is something like this:

DMZDomain\SharepointSQLUser

InternalDomain\SQLServiceUser

The DMZDomain would rarely be trusted by the InternalDomain but the InternalDomain would often be trusted by the DMZDomain if communication were allowed between them..

That error message is pretty clear, sharepoint is trying to use a login that is not trusted by the domain. As a side note I think I have seen this error when logged into a local account on a machine that was then trying to use trusted authentication to SQL.

CEWII