If you have actually deleted the 'root' user, I would check out this question for MAMP. There is a generic article detailing the same essential steps here.
Note that the #1045 Access Denied is a generic response that can apply to both a user that doesn't exist as well as simply using an incorrect password. So I would attempt to double-check that root really doesn't exist with a password reset attempt before forging on to replacing the root user account for MySQL.