The problem here is with the definition of 'dead'. A dead man is a man separated. If you are physically dead, you are separated from your body. Your body may be discarded and rotting, but you go on. If you are spiritually dead, you are separated from God. You are not spiritually rotting or unconscious.
A man goes to hell not for sinning, according to the Bible, but for refusing to believe in Christ as Savior and Redeemer and God Himself. This is not only explicitely stated in John 3:16-21, but by Jesus Himself when talking to the Jews in John 8:23-25:
But he continued, "You are from below; I am from above. You are of this world; I am not of this world. I told you that you would die in your sins; if you do not believe that I am [the one I claim to be] [note: the Greek here is the double 'I am' -- ego eimi -- translated I am I am], you will indeed die in your sins."
"Who are you?" they asked.
"Just what I have been claiming all along," Jesus replied.
In other words, an unbeliever dies IN his sins, but is not condemned BECAUSE of them. What he is condemned for is unbelief:
"For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. For God did not send his Son into the world to condemn the world, but to save the world through him. Whoever believes in him is not condemned, but whoever does not believe stands condemned already because he has not believed in the name of God's one and only Son. This is the verdict: Light has come into the world, but men loved darkness instead of light because their deeds were evil. Everyone who does evil hates the light, and will not come into the light for fear that his deeds will be exposed. But whoever lives by the truth comes into the light, so that it may be seen plainly that what he has done has been done through God."
If you cross reference this with Romans 1, you will see that God's anger is being poured out on those who SUPPRESS the truth. In other words, it is what you do with the truth that you are presented with which will make all the difference in the long run. If you live by the truth that you know, God the Father will lead you to the Son, and you can either accept or reject Him. If you prefer the lie, then that is what you will get, and with it the consequence of that lie: condemnation.