Here's the scripture regarding being born dead in sin:
Eph 2:1) And you
hath he quickened, who were dead in trespasses and sins;
Eph 2:5) Even when we were dead in sins, hath quickened us together with Christ, (by grace ye are saved
Col 2:13) And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him, having forgiven you all trespasses;
Being born dead in sin does not mean we cannot choose to believe on Jesus Christ.