The day I meet an atheist who correctly understands the moral argument will be the day I drop dead of a heart attack. A frustratingly common straw man of the argument is that Christians claim atheists cannot do good things, or that they need God to tell them what is right and what is wrong, or even that they should do bad things if they don't believe in God. This is not, nor has it ever been, the moral argument. Rather, the argument is that if atheism is correct, then whatever an atheist does, there is no objective standard by which those actions can be considered "good" or "evil".
The Bible actually testifies that unbelievers can, and indeed very often do, have a well-designed conscience. God did not drop man in one place, morality in another, and expect us to go searching for His book in order to find out what's good and what's evil. Rather, the book of Romans tells us that man has the law "written on our hearts". Thus, even if you have never read the Bible, or even if you have never been exposed to a culture that has been even remotely shaped by Christianity, you will have at least some kind of awareness of morality. Ironically, this means on Judgement Day, you will be judging yourself.
But here's the problem: If atheism is true, your moral instincts are really nothing more than your own personal preferences. Currently, as always, our world is filled with moral debates. Gay "marriage", abortion, religious liberty, these are just a few topics that are a lot more controversial than they ought to be. But if there is no God, these questions are equal to the question of whether or not it is acceptable to put pineapple on pizza. You have your opinion, I have mine, and neither of us is really right.
Is this the case? Are moral issues really just a matter of personal preference? If you want to say yes, then fair enough. Continue suppressing your natural instincts and stew in the awkwardness of the fact you now must claim that there is no moral distinction between yourself and Adolf Hitler. The moral argument was not designed for you, and there are plenty of other arguments that establish the truth of Christianity.
But let's suppose you are still mentally stable enough to recognise that moral laws are objective, and not just a matter of personal preference. That means two things. First, legislation requires a legislature. Just as you cannot call a thing illegal in a region with no government, you cannot call a thing immoral if there is no God. Second, it means you are not that moral legislature. What is evil now was evil before you were born, and will continue to be evil after you have served your time on earth and stood in the court of the Lord. The same applies to what is good.
But let's be honest: You've been living as if you were that moral legislature. That which you, personally, have a preference for is what you have been advocating for. In fact, in this day and age, the chances are quite high that you have even used the fact that the Bible does not fit your moral preferences as an argument against it. So, you are not God, yet have been living as if you are. This is called sin. The penalty for this treason? Death.
But God takes no pleasure in the death of the wicked. Rather, He prefers the wicked turn from their sin and live. Thus, He has given you the opportunity to do so. 2,000 years ago, Jesus Christ, the Son of God, came to the Earth as a man, lived a perfect life, and died on the cross as if He was a sinner. As if He was you. Because of this, you can be judged as if you were Him. The sins you have committed can be completely forgotten, and all it takes is faith. Confess Jesus as Lord, and believe He rose from the dead, and instead of condemning you for your treason, God will grant you eternal life in His Kingdom.