This sounds like a local VM configuration issue, not a Kentico one.
Any time we encounter SQL Server connection issues it's either because:
- Network connection issues
- SQL Server Windows service is offline
- SQL Server login doesn't exist even though the database user does
- SQL Server doesn't actually have a Kentico database
- SQL Server login password is incorrect
- Windows user doesn't have permissions to login to the database/server
Can you login to SSMS with the user you are attempting to use Windows authentication with?
Does this user have access to the Kentico database?
Try creating a non-Kentico ASP.NET application and use the same Windows auth connection string to the same Kentico database and try to run a SQL query against it. If this doesn't work, then the problem is definitely on the SQL/auth side and not Kentico.