This might seem obvious but I've had this error when trying to use LINQ to SQL with my business logic in a separate class library project.
I've created the DBML in a class library, with all my business logic and custom controls in this project. I'd referenced the class library from my web project and attempted to use it directly from the web project.
The error indicated the login failed for my user name. My user name and password were correct, but the fix was to copy my connection string to the correct location. I've learned the issue from another site and thought I would make a note here.
Error: Login failed for user 'username' System.Data.SqlClient.SqlException