The error message is pretty explicit!
The server was not found or was not accessible. Verify that the instance name is correct and that SQL Server is configured to allow remote connections.
And it means what it says: the SQL server you are trying to access - a local DB - is not installed or is not running.
It's unlikely that an SQL server instance for a website will be LOCALDB - it's normally a named instance, and it almost certainly won't use integrated security, particularly on a shared hosting service. Also remember that IIS doesn't run under your user account, so SQL need to be configured to work with it.
So start by looking at your DB information from your provider, and then try this: Simple SQL Connection String Creation
Oh, and by the way ... attaching a DB is only for development, it only works on SQL Express and can't be used in production. Add that to the IIS user problem and you would probably get "Access violation" errors trying to attach the DB for your website anyway. The DB should be installed into SQL and used directly, not attached.