The argument from morality is undoubtedly one of the most powerful arguments. In the words of William Lane Craig, "it hits people where they live", not showing that God exists, but showing that even the most vehement unbeliever is already subconsciously aware that He does. In atheistic worldviews, morality is baseless. It is a set of subjective preferences to which we would bind the world. I like this behaviour, therefore I call it good. I don't like this behaviour, therefore I call it bad. Without God, these are nothing short of personal opinions with no power over the rest of humanity. Only God can give morality objective meaning.
Most atheists object to this, and provide a number of reasons they think morality is objective even without God. At the heart of it, every single one of these objections proves the original argument true. No atheist has ever been able to show why, if there is no God, human beings should behave in a particular way, much less that our particular Western brand of morality is the correct one. Atheists often butt heads even amongst each other, with no clear winner in any scenario. In the end, they might put it to a vote, with the loser still maintaining their own opinion and believing the winner to be wrong.
So in atheism, there is no objective morality, even though the majority of them will not admit that. The problem is, some of them willingly admit this. If there is no God, they admit there is no morality, which means they cannot even show that their own lives matter. These very same atheists will argue quite passionately in favour of abominable practices, such as abortion.
The Bible says that those who reject God, ultimately, will be likewise rejected by Him. As they increase in their sin, God gives them over to their sins. This is especially seen in the opening chapters of the Book of Romans. Here, we see that creation itself reveals God to us, and that He has created us with an inbuilt conscience. An atheist does not need God's direct revelations to know there is such a thing as morality, because God has "written it on their hearts". Morality is an instinct. Furthermore, creation reveals God's invisible attributes. There is the initial "wow" factor caused by a surface look, and as we study creation in depth, we see too much evidence for Him to deny Him. This is especially shown by the case of Anthony Flew. Though he never came to Christ, he nevertheless became a Theist when he found out about DNA, which simply would never have come into being by unaided natural processes.
But obviously, not all atheists even go that far. They will invoke things like "God of the gaps", and look for any answer except God. This stubborn rejection, which is by no means based on the intellect, ultimately results in God giving the atheist over to a depraved mind. They become almost animalistic in their thinking, not obeying their conscience, but instead doing what gives them and their allies the most pleasure. We read about the results near the end of Romans 1, and it almost perfectly describes the modern world.
This really ought to show us our need for God. It is not that we need specific knowledge of God in order to be motivated to do good, or even to use the moral instincts He implemented in us at our conception, but that ultimately, if we do not use those moral instincts, we lose them. The fact that we live in a world in which a man can argue more vehemently in favour of killing the weakest and most innocent members of society than for why we should not kill him really ought to show us what's at stake here. Man, without God, is beyond depraved.
Of course, in the flesh, even God is, in a sense, "not enough" to completely stop the flow of sin. Human beings are rotten to the core, and so the only way to truly kill sin is to kill the sinner. A time will come when that very thing will happen. Every human being will one day die and face God in judgement. The problem is, we've all thought, said and done things that result in death. Yet God, in His infinite love, has provided an alternative. There is a way to not only survive judgement day, but actually benefit from it. 2,000 years ago, one man walked the earth who did not sin. This man was Jesus Christ, the Son of God, and He died on a cross. There, He took the full wrath of God for sin. And yet, He did not stay dead. On the third day, He rose again. All who will repent of their sin, confess Him as Lord, and believe He rose from the dead will be saved.