From my mini commentary of sorts on Romans 7 from another answer:
But sin taking occasion by the commandment, wrought in me all manner of concupiscence. For without the law sin was dead.—Taking occasion by the knowledge (having the law) that something truly is sinful, it makes what may otherwise have been a venial offense (not having full knowledge of the thing's sinfulness) a mortal, that is, damnable sin. (1 Jn 5:16-17).
I'll add to this that "taking occasion" implies a personification, as it were, of sin, where sin 'wants' to convict the sinner, and make sinners out of otherwise innocent men.
This is why St. Paul says that when there is no law to 'vindicate,' or 'back up' sin in its quest to entrap men in it, it is "dead," having no force or consequence (inasmuch as where there is no guilty, there is really no sin). No 'impact.'
Similar to how death (sometimes synonymous with sin in St. Paul's discourses when it comes to the sin of Adam and its consequences) is left without its 'sting' whenever Christ's grace is in the soul, which liberates it from just punishment (eternal damnation):
1 Corinthians 15:55-56 (ASV)
O death, where is thy victory? O death, where is thy sting? [Now] the sting of death is sin; and the power of sin is the law:
Now the sting of death is sin: and the power of sin is the law. Here 'power' and 'sting' stand for their ability to take hold of a person and cause them harm. Their impact. As said before, the impact of sin is taken away where the law isn't there to enforce justice at least so as to be able to convict sinners as held to it as a standard.
'The ability of sin to do damage to a soul lies in the fact that there was a law there to convict them, and thus provide perfect knowledge of the sinfulness of the sin on his part.'
The 'impact' of death is its right to take one who sins. Physically, or eternally. It's fallacious to claim, however, that death cannot exist without sin. For example, Jesus' death. (Arguably Mary's :])
Romans 5:13-15 (ASV)
For until the law sin was in the world; but sin is not imputed when there is no law. Nevertheless death reigned from Adam until Moses, even over them that had not sinned after the likeness of Adam's transgression, who is a figure of him that was to come. But not as the trespass, [is the gift also]. For if by the trespass of the one the many died, much more did the grace of God, and the gift by the grace of the one man, Jesus Christ, abound unto the many.
That is, in original sin, death passes to all. Original, because by nature. Passed on to all regardless of their not having transgress as Adam did, because not of a separate nature than fallen, sinful Adam (Gn 5:3) (typologically, this could have been derived from the fact of the spiritual headship of Christ which allows us to escape sin, rather than live as born in it)
St. Paul compares the transgression of one man, and guilt passing to all men, and Jesus Christ, "the last Adam," (1 Cor 15:45) of whom Adam was a type, and guilt passing from all men. Yet the respective results of the actions of the two Adams differ in that the latter is a bestowal of grace and reconstitution in it, and not a privation of it.
Thus, these texts are not at odds, because they do not contradict one another.