Can we really be good without God? In a way, the answer is yes. A lack of faith in God is certainly a good way to justify depravity, but let's be honest here: Some unbelievers are the nicest people you can know. There are even those who admit they prefer the Christian view of morality.
But in the other sense, the answer is no. Good and evil, Biblically speaking, are different from the cultural standard thereof. Whereas man sees good as that which benefits man, whether individually or as a whole, God sees good as that which furthers His Kingdom.
Imagine a profitable company. The company will naturally pay its more profitable workers more, but no matter how profitable members of a rival company are, it will (presumably) never pay them. In this scenario, the goodness of the worker does not matter, but the association, or lack thereof, with the company.
God works in a similar way. (There is more to it, of course, but we're simplifying it for sake of analogy). It's one thing to be able to do good for non-Godly purposes, but because of the non-Godly purposes, they're not really "good" in the eyes of God. The Bible actually describes our righteous acts as "filthy rags" (Isaiah 64:6) because of our sin. Sin is what makes us part of the rival company. The rival company which happens to thrive off resources stolen from God in the first place. How, then, could one possibly hope to be "good" without God? A KFC employee would have more luck convincing Chick-Fil-A to pay them for their skills than an unbeliever would have convincing God to grant him eternal life.