What do you predict would happen if hydrogen bonds formed between any two nitrogenous bases in DNA?

Well, since they don't in the world as we know it (as far as I know) the laws of physics that govern hydrogen bonding would have to be different in order to allow it. This would have very far reaching and unfathomable consequences far beyond genetics; suffice it to say the universe would be so very different that there probably would be no nitrogenous bases, or DNA for that matter. So, it just can't happen since "What it it did?" implies that it wouldn't.