Can a sinner consecrate his life to God? Yes, but not while he remains a sinner. Consecration is not the first step of the Christian life. To do your first work as a Christian is to repent. Jesus said, “Repent, for the kingdom of heaven is at hand.” He didn't say, “Consecrate yourself.” He said, “Repent.”
To repent is to really give up sinning. The Bible also calls repentance “crucifixion,” or “dying with Christ.” Practically, it means that you seriously aim at a sinless life. The Bible usually includes a verbal, detailed confession of your sins to God as part of repentance.
Many sinners stumble because they're trying to be Christians, but they never did their first work. Perhaps you've done this. Have you tried to serve God, but skipped over getting on your face and telling God exactly how wicked you are? How can you serve God if you still serve sin? You cannot. This is why the Apostle Paul speaks first of dying with Christ, and second of yielding the new life in Christ to God. Until you're born again, you don't have a new life that you can consecrate to Jesus.
Without this first work, you cannot be on the way to heaven. Instead, the law of God right now condemns you. You may have once repented, but now you are cold and backslidden. You've left the church and gone into sin. Or, you've remained in the church, but you've taken back your consecration to God and backslid in your heart. Now you are a cold, religious shell, without feeling for Jesus.
There is no salvation outside of a present salvation from sin! If you aren't walking in obedience to Jesus today, don't stop and wonder whether you've ever been born again or not. Instead, confess your sins out loud to God and do your first work of repentance!