To say that Baptism “connects us to Christ” is to say that prior to our Baptism, we were disconnected from Christ. Scripture confirms this in no uncertain terms. Fortunately, God's work in and through Baptism is to connect us to Christ's death and resurrection.
Note the contrast. We were dead in our trespasses and sins. Now, God has raised us to new life in and through Baptism. This new life is a life in which we no longer live for ourselves, but for Christ, who reconciled us to God. It is a life in which we no longer live to gratify our sinful desires, but rather live to please our gracious God by serving our fellow man.