Ah, so your problem was about the System Transfer. Well, that's not better. Because as I said, you can't link a new NNID without unlinking the old one, and you can't unlink the old one without wiping your saves, which isn't what you want, and you also lost your bought games in the meantime.
And that's yet another time when I want to say that hacks are not only for piracy... Yeah, I already said that, but really. If your current 3DS was hacked, you could have dumped its movable.sed and injected it on the New 3DS, which would have allowed you to use the "Nintendo 3DS" folder from your current 3DS on your New one, so all your games and saves are still here... But I guess it's not hacked and it's on 11.0, right?
Well in that case, if you're going to use the New 3DS and can't recover your NNID password, sorry to tell you but all the games you bought are gone forever, no way to get them back (a new NNID won't help) except by paying again (or less honest options -.-).
And at least, to lose only your games and not your saves, use JKSM on the old 3DS to backup saves and use it again on the New one to restore them. And really, if you plan on forgetting the password for the new NNID too, getting a CFW on the New 3DS would not be the worst idea. So you can always get out of situations like this one, it's not just for piracy, once again. And that's also one of the reasons why I buy cartridges, not digital...