I would agree with Chris, and add something: you can always use "n'avoir pas de", but "n'avoir aucun" can only be used with something you can count. Example: OK: Je n'ai pas de temps. (I have no time) But not: Je n'ai aucun temps. Think of it as the English: "much time", but not "many time"; time is not a definite quantity OK: Je n'ai pas d'argent. (I have no money) But not: Je n'ai aucun argent. Same here, "much money", but not "many money"; you cannot quantify money either OK: Je n'ai pas de chat. (I have no cat) Also OK: Je n'ai aucun chat. (I have no cat) I am not sure if it is grammatically wrong, but it sure sounds weird to me as a native of metropolitan French.

Je n'ai aucun/aucune is more emphatic. = I don't have even one of ....

In a similar way ne...que emphasizes the smallness or limitations of something ... J'ai un chat. (I have a cat.) Ma soeur a sept chats, mais je n'ai qu'un chat. (My sister has seven cats, but I only have one cat.) Ma soeur a sept chats, mais je n'en ai qu'un. Je n'ai pas de chat. (I have no cats. I don't have a cat.) Ma soeur a sept chats, mais je n'ai aucun chat. (My sister has seven cats, but I don't have any cats at all.) Ma soeur a sept chats, mais je n'en ai aucun.